{"id":"act_quizme:math:q1:04","source_id":"act_quizme","source_item_id":"math-q1-04","external_id":"b1c6a99c7b199f12","program":"ACT","section":"math","category_code":null,"category":null,"subcategory_code":null,"subcategory":null,"form_id":null,"passage_id":null,"position":4,"scored":true,"layout_warning":null,"stem":"In △ABC, ∠A and ∠C are congruent, and the measure of ∠B is 143.6°. What is the measure of ∠A?","stimulus":"","stimulus_html":null,"stem_html":"<div class=\"math-question-wrap\"><p>In △ABC, ∠A and ∠C are congruent, and the measure of ∠B is 143.6°. What is the measure of ∠A?</p>\n</div>\n<div><div class=\"math-answer-select-wrap\"></div></div>","rationale_html":"<p><strong>F.</strong> <strong>Correct.</strong> The measures of angles in a triangle sum to 180°, so in △ABC, <span style=\"white-space: nowrap;\"><math><mi>m</mi><mo>∠</mo><mi>A</mi><mo>+</mo><mi>m</mi><mo>∠</mo><mi>B</mi><mo>+</mo><mi>m</mi><mo>∠</mo><mi>C</mi><mo>=</mo><mn>180</mn><mo>°</mo></math>.</span> Since <span style=\"white-space: nowrap;\"><math><mo>∠</mo><mi>A</mi><mo>≅</mo><mo>∠</mo><mi>C</mi></math>,</span> <span style=\"white-space: nowrap;\"><math><mi>m</mi><mo>∠</mo><mi>A</mi><mo>=</mo><mi>m</mi><mo>∠</mo><mi>C</mi></math>.</span> Substituting this relationship and&nbsp;<math><mi>m</mi><mo>∠</mo><mi>B</mi><mo>=</mo><mn>143</mn><mo lspace=\"0\" rspace=\"0\">.</mo><mn>6</mn><mo>°</mo></math>&nbsp;into the initial equation yields <span style=\"white-space: nowrap;\"><math><mi>m</mi><mo>∠</mo><mi>A</mi><mo>+</mo><mn>143</mn><mo lspace=\"0\" rspace=\"0\">.</mo><mn>6</mn><mo>°</mo><mo>+</mo><mi>m</mi><mo>∠</mo><mi>A</mi><mo>=</mo><mn>180</mn><mo>°</mo></math>.</span> Subtract 143.6° from each side of the equation and divide each side by 2 to calculate <span style=\"white-space: nowrap;\"><math><mi>m</mi><mo>∠</mo><mi>A</mi><mo>=</mo><mo>(</mo><mfrac><mrow><mn>180</mn><mo>-</mo><mn>143</mn><mo lspace=\"0\" rspace=\"0\">.</mo><mn>6</mn></mrow><mn>2</mn></mfrac><mo>)</mo><mo>°</mo><mo>=</mo><mn>18</mn><mo lspace=\"0\" rspace=\"0\">.</mo><mn>2</mn><mo>°</mo></math>.</span></p><p><strong>G.</strong> <strong>Incorrect.</strong> You may have started correctly by subtracting&nbsp;<math><mi>m</mi><mo>∠</mo><mi>B</mi><mo>=</mo><mn>143</mn><mo lspace=\"0\" rspace=\"0\">.</mo><mn>6</mn><mo>°</mo></math>&nbsp;from <span style=\"white-space: nowrap;\"><math><mn>180</mn><mo>°</mo></math>.</span> Then, remember that the difference, 36.4°, is twice the measure of the desired angle since the remaining two angles are congruent. Try dividing your answer by 2.</p><p><strong>H.</strong> <strong>Incorrect.</strong> You may have thought that&nbsp;<math><mi>m</mi><mo>∠</mo><mi>A</mi><mo>+</mo><mi>m</mi><mo>∠</mo><mi>C</mi><mo>=</mo><mn>143</mn><mo lspace=\"0\" rspace=\"0\">.</mo><mn>6</mn><mo>°</mo></math>&nbsp;so that <span style=\"white-space: nowrap;\"><math><mn>2</mn><mo>(</mo><mrow><mi>m</mi><mo>∠</mo><mi>A</mi></mrow><mo>)</mo><mo>=</mo><mn>143</mn><mo lspace=\"0\" rspace=\"0\">.</mo><mn>6</mn><mo>°</mo><mo>↔</mo><mi>m</mi><mo>∠</mo><mi>A</mi><mo>=</mo><mn>71</mn><mo lspace=\"0\" rspace=\"0\">.</mo><mn>8</mn><mo>°</mo></math>.</span> Remember that the given angle measure is <span style=\"white-space: nowrap;\"><math><mi>m</mi><mo>∠</mo><mi>B</mi></math>,</span> <strong>not</strong> <span style=\"white-space: nowrap;\"><math><mi>m</mi><mo>∠</mo><mi>A</mi><mo>+</mo><mi>m</mi><mo>∠</mo><mi>C</mi></math>.</span></p><p><strong>J.</strong> <strong>Incorrect.</strong> You may have thought that <span style=\"white-space: nowrap;\"><math><mi>m</mi><mo>∠</mo><mi>A</mi><mo>=</mo><mi>m</mi><mo>∠</mo><mi>B</mi></math>.</span> Be sure to carefully read the given information.</p>","correct_answer":["F"],"equiv_key":"48159e894ea7df8742cc479d","has_media":false,"has_mathml":true,"has_table":false,"section_label":"Mathematics","options":[{"label":"F","content_html":"<p>18.2°</p>","ord":0},{"label":"G","content_html":"<p>364°</p>","ord":1},{"label":"H","content_html":"<p>71.8°</p>","ord":2},{"label":"J","content_html":"<p>143.6°</p>","ord":3}],"passage":null,"attribution":{"source_id":"act_quizme","source_name":"ACT QuizMe official practice questions","rights_holder":"ACT Education Corp.","canonical_url":"https://quizme.act.org/","retrieved_from":"https://quizme.act.org/","attribution":"Official ACT practice questions © ACT Education Corp., from the QuizMe practice quizzes at quizme.act.org.","disclaimer":"ACT® is a registered trademark of ACT Education Corp., which is not affiliated with, does not sponsor, and does not endorse this project.","license":"ACT Education Corp. copyright. Published free on the public web; not licensed for redistribution.","redistributable":false,"item_count":78},"equivalents":[]}