In the figure above, segments AE and BD are parallel. If angle BDC measures 58° and angle ACE measures 62°,

Question

In the figure above, segments AE and BD are parallel. If angle BDC measures 58&deg; and angle ACE measures 62&deg;, what is the measure of angle CAE ?

Accepted Answer

Choice B is correct. It&rsquo;s given that angle ACE measures . Since segments AE and BD are parallel, angles BDC and CEA are congruent. Therefore, angle CEA measures . The sum of the measures of angles ACE , CEA , and CAE is since the sum of the interior angles of triangle ACE is equal to . Let the measure of angle CAE be . Therefore, , which simplifies to . Thus, the measure of angle CAE is . Choice A is incorrect. This is the measure of angle A EC , not that of angle CAE . Choice C is incorrect. This is the measure of angle ACE , not that of CAE . Choice D is incorrect. This is the sum of the measures of angles ACE and CEA .

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