Angles and Parallel Lines
<p><a href="https://www.prepswift.com/quizzes/quiz/prepswift-angles-and-parallel-lines" target="_blank">Angles and Parallel Lines Exercise</a></p><p><strong><span style="color:#27ae60;">Explanation of What You're Looking at Below</span></strong></p>
<p>In the diagram, lines $l$ and $m$ are parallel, meaning that they never touch (at least in the math we're doing). If you ever want to have your mind freakin' BLOWN, read about non-Euclidean geometry. <span style="color:#e74c3c;">But after your GRE test</span>. Not now.</p>
<p>Anyway, lines $l$ and $m$ are parallel. If we intersect those two parallel lines with another line, we get the following angle relationships. Memorize this. It's important. Note that angles $a$ and $b$ are supplementary. </p>
<center><svg height="209.51998901367188" style="
width:661.9199829101562px;
height:209.51998901367188px;
background: #FFF;
fill: none;
" width="661.9199829101562" x="0" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" y="0"> <svg class="role-diagram-draw-area" xmlns="http://www.w3.org/2000/svg"><g class="shapes-region" style="stroke: black; fill: none;"><g class="arrow-line"><path class="connection real" d=" M438.6,20.26 L200,76" stroke-dasharray="" style="stroke: rgb(0, 0, 0); stroke-width: 1; fill: none; fill-opacity: 1;"></path></g><g class="arrow-line"><path class="connection real" d=" M457.6,100.26 L219,156" stroke-dasharray="" style="stroke: rgb(0, 0, 0); stroke-width: 1; fill: none; fill-opacity: 1;"></path></g><g class="arrow-line"><path class="connection real" d=" M321.6,16.26 L283.6,186.26" stroke-dasharray="" style="stroke: rgb(0, 0, 0); stroke-width: 1; fill: none; fill-opacity: 1;"></path></g><g></g></g><g></g><g></g><g></g></svg> <svg height="207.59999084472656" style="width:660px;height:207.59999084472656px;font-family:Asana-Math, Asana;background:#FFF;" width="660" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g><g><g><g transform="matrix(1,0,0,1,185.95999145507812,83.63999938964844)"><path d="M251 722L239 733C187 707 151 698 79 691L75 670L123 670C147 670 157 663 157 648C157 645 157 640 154 622C143 567 70 182 55 132C42 82 36 52 36 31C36 6 47 -9 66 -9C92 -9 128 12 226 85L216 103L190 86C161 67 139 56 129 56C122 56 116 66 116 76C116 82 117 89 120 104Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,187.95999145507812,163.63999938964844)"><path d="M730 103L704 86C675 67 653 56 643 56C636 56 630 65 630 76C630 86 632 95 637 116L712 413C716 430 719 446 719 454C719 471 709 482 693 482C664 482 626 464 565 421C502 376 467 341 418 272L448 409C452 429 455 444 455 451C455 470 445 482 429 482C399 482 353 460 298 418C254 384 234 363 169 275L202 408C206 424 208 439 208 451C208 470 199 482 185 482C164 482 126 461 52 408L24 388L31 368C68 391 103 414 110 414C121 414 128 404 128 389C128 338 87 145 46 2L49 -9L117 6L139 108C163 219 190 278 245 338C287 384 332 414 360 414C367 414 371 406 371 393C371 358 349 244 308 69L292 2L297 -9L366 6L387 113C403 194 437 269 481 318C536 379 586 414 618 414C626 414 631 405 631 389C631 365 628 351 606 264C566 105 550 84 550 31C550 6 561 -9 580 -9C606 -9 642 12 740 85Z" fill="rgb(0,0,0)" fill-opacity="1" stroke="rgb(0,0,0)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,298.9599914550781,46.63999938964844)"><path d="M271 204L242 77C238 60 236 42 236 26C236 4 245 -9 260 -9C283 -9 324 17 406 85L399 106C375 86 346 59 324 59C315 59 309 68 309 82C309 87 309 90 310 93L402 472L392 481L359 463C318 478 301 482 274 482C246 482 226 477 199 464C137 433 104 403 79 354C35 265 4 145 4 67C4 23 19 -11 38 -11C75 -11 155 41 271 204ZM319 414C297 305 278 253 244 201C187 117 126 59 94 59C82 59 76 72 76 99C76 163 104 280 139 360C163 415 186 433 234 433C257 433 275 429 319 414ZM642 689C560 689 493 622 493 539C493 456 560 389 643 389C724 389 793 457 793 537C793 621 726 689 642 689ZM642 649C703 649 753 599 753 537C753 479 703 429 643 429C582 429 533 478 533 539C533 600 582 649 642 649Z" fill="rgb(74,144,226)" fill-opacity="1" stroke="rgb(74,144,226)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,316.9599914550781,65.63999938964844)"><path d="M271 204L242 77C238 60 236 42 236 26C236 4 245 -9 260 -9C283 -9 324 17 406 85L399 106C375 86 346 59 324 59C315 59 309 68 309 82C309 87 309 90 310 93L402 472L392 481L359 463C318 478 301 482 274 482C246 482 226 477 199 464C137 433 104 403 79 354C35 265 4 145 4 67C4 23 19 -11 38 -11C75 -11 155 41 271 204ZM319 414C297 305 278 253 244 201C187 117 126 59 94 59C82 59 76 72 76 99C76 163 104 280 139 360C163 415 186 433 234 433C257 433 275 429 319 414ZM642 689C560 689 493 622 493 539C493 456 560 389 643 389C724 389 793 457 793 537C793 621 726 689 642 689ZM642 649C703 649 753 599 753 537C753 479 703 429 643 429C582 429 533 478 533 539C533 600 582 649 642 649Z" fill="rgb(74,144,226)" fill-opacity="1" stroke="rgb(74,144,226)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,279.9599914550781,137.63999938964844)"><path d="M271 204L242 77C238 60 236 42 236 26C236 4 245 -9 260 -9C283 -9 324 17 406 85L399 106C375 86 346 59 324 59C315 59 309 68 309 82C309 87 309 90 310 93L402 472L392 481L359 463C318 478 301 482 274 482C246 482 226 477 199 464C137 433 104 403 79 354C35 265 4 145 4 67C4 23 19 -11 38 -11C75 -11 155 41 271 204ZM319 414C297 305 278 253 244 201C187 117 126 59 94 59C82 59 76 72 76 99C76 163 104 280 139 360C163 415 186 433 234 433C257 433 275 429 319 414ZM642 689C560 689 493 622 493 539C493 456 560 389 643 389C724 389 793 457 793 537C793 621 726 689 642 689ZM642 649C703 649 753 599 753 537C753 479 703 429 643 429C582 429 533 478 533 539C533 600 582 649 642 649Z" fill="rgb(74,144,226)" fill-opacity="1" stroke="rgb(74,144,226)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,297.9599914550781,154.63999938964844)"><path d="M271 204L242 77C238 60 236 42 236 26C236 4 245 -9 260 -9C283 -9 324 17 406 85L399 106C375 86 346 59 324 59C315 59 309 68 309 82C309 87 309 90 310 93L402 472L392 481L359 463C318 478 301 482 274 482C246 482 226 477 199 464C137 433 104 403 79 354C35 265 4 145 4 67C4 23 19 -11 38 -11C75 -11 155 41 271 204ZM319 414C297 305 278 253 244 201C187 117 126 59 94 59C82 59 76 72 76 99C76 163 104 280 139 360C163 415 186 433 234 433C257 433 275 429 319 414ZM642 689C560 689 493 622 493 539C493 456 560 389 643 389C724 389 793 457 793 537C793 621 726 689 642 689ZM642 649C703 649 753 599 753 537C753 479 703 429 643 429C582 429 533 478 533 539C533 600 582 649 642 649Z" fill="rgb(74,144,226)" fill-opacity="1" stroke="rgb(74,144,226)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,319.9599914550781,42.63999938964844)"><path d="M235 722L223 733C171 707 135 698 63 691L59 670L107 670C131 670 141 663 141 646C141 639 140 628 139 622L38 71C37 68 37 64 37 61C37 22 85 -11 140 -11C177 -11 228 8 271 39C367 107 433 244 433 376C433 414 424 453 412 468C405 477 392 482 377 482C353 482 323 474 295 460C244 433 211 403 149 324ZM322 424C348 424 361 401 361 352C361 288 340 202 310 137C277 68 237 36 183 36C137 36 112 59 112 101C112 135 127 276 208 361C241 395 293 424 322 424ZM661 689C579 689 512 622 512 539C512 456 579 389 662 389C743 389 812 457 812 537C812 621 745 689 661 689ZM661 649C722 649 772 599 772 537C772 479 722 429 662 429C601 429 552 478 552 539C552 600 601 649 661 649Z" fill="rgb(208,2,27)" fill-opacity="1" stroke="rgb(208,2,27)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,294.9599914550781,68.63999938964844)"><path d="M235 722L223 733C171 707 135 698 63 691L59 670L107 670C131 670 141 663 141 646C141 639 140 628 139 622L38 71C37 68 37 64 37 61C37 22 85 -11 140 -11C177 -11 228 8 271 39C367 107 433 244 433 376C433 414 424 453 412 468C405 477 392 482 377 482C353 482 323 474 295 460C244 433 211 403 149 324ZM322 424C348 424 361 401 361 352C361 288 340 202 310 137C277 68 237 36 183 36C137 36 112 59 112 101C112 135 127 276 208 361C241 395 293 424 322 424ZM661 689C579 689 512 622 512 539C512 456 579 389 662 389C743 389 812 457 812 537C812 621 745 689 661 689ZM661 649C722 649 772 599 772 537C772 479 722 429 662 429C601 429 552 478 552 539C552 600 601 649 661 649Z" fill="rgb(208,2,27)" fill-opacity="1" stroke="rgb(208,2,27)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,300.9599914550781,132.63999938964844)"><path d="M235 722L223 733C171 707 135 698 63 691L59 670L107 670C131 670 141 663 141 646C141 639 140 628 139 622L38 71C37 68 37 64 37 61C37 22 85 -11 140 -11C177 -11 228 8 271 39C367 107 433 244 433 376C433 414 424 453 412 468C405 477 392 482 377 482C353 482 323 474 295 460C244 433 211 403 149 324ZM322 424C348 424 361 401 361 352C361 288 340 202 310 137C277 68 237 36 183 36C137 36 112 59 112 101C112 135 127 276 208 361C241 395 293 424 322 424ZM661 689C579 689 512 622 512 539C512 456 579 389 662 389C743 389 812 457 812 537C812 621 745 689 661 689ZM661 649C722 649 772 599 772 537C772 479 722 429 662 429C601 429 552 478 552 539C552 600 601 649 661 649Z" fill="rgb(208,2,27)" fill-opacity="1" stroke="rgb(208,2,27)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g></g></g><g><g><g><g transform="matrix(1,0,0,1,273.9599914550781,159.63999938964844)"><path d="M235 722L223 733C171 707 135 698 63 691L59 670L107 670C131 670 141 663 141 646C141 639 140 628 139 622L38 71C37 68 37 64 37 61C37 22 85 -11 140 -11C177 -11 228 8 271 39C367 107 433 244 433 376C433 414 424 453 412 468C405 477 392 482 377 482C353 482 323 474 295 460C244 433 211 403 149 324ZM322 424C348 424 361 401 361 352C361 288 340 202 310 137C277 68 237 36 183 36C137 36 112 59 112 101C112 135 127 276 208 361C241 395 293 424 322 424ZM661 689C579 689 512 622 512 539C512 456 579 389 662 389C743 389 812 457 812 537C812 621 745 689 661 689ZM661 649C722 649 772 599 772 537C772 479 722 429 662 429C601 429 552 478 552 539C552 600 601 649 661 649Z" fill="rgb(208,2,27)" fill-opacity="1" stroke="rgb(208,2,27)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g></g></g></svg> </svg></center>