Question

triangle a has angles that measure 36° and 82°.triangle b has the angle measures shown below.which statement is true about triangle a and triangle b?the triangles are similar because they each have angles that measure 36°, 62°, 82°.the triangles are not similar because an 82° angle is not congruent to a 62° angle.the triangles are not similar because one of them has an obtuse angle.the triangles are similar because they each have only acute angles.

Explanation:

Step1: Find the third angle of Triangle B

The sum of an exterior angle and its adjacent interior angle is \(180^{\circ}\). So the interior angle adjacent to \(144^{\circ}\) is \(180 - 144=36^{\circ}\).
Using the angle - sum property of a triangle (\(A + B + C=180^{\circ}\)), let the third angle of Triangle B be \(x\). We know two angles: \(62^{\circ}\) and \(36^{\circ}\). Then \(x=180-(62 + 36)=82^{\circ}\).

Step2: Compare angles of Triangle A and Triangle B

Triangle A has angles \(36^{\circ}\), \(62^{\circ}\), \(82^{\circ}\). Triangle B has angles \(36^{\circ}\), \(62^{\circ}\), \(82^{\circ}\).
By the AA (Angle - Angle) similarity criterion (if two angles of one triangle are equal to two angles of another triangle, the triangles are similar), since all three angles of Triangle A are equal to all three angles of Triangle B.

Answer:

The triangles are similar because they each have angles that measure \(36^{\circ}\), \(62^{\circ}\), \(82^{\circ}\).