Question

triangle abc and triangle def are similar. in triangle abc, m∠a = 82°. in triangle def, m∠f = 67°. what are m∠e and m∠g? m∠e = □° m∠g = □°

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°.

Step2: Find ∠B in △ABC

Since △ABC and △DEF are similar, corresponding angles are equal. But we first find the third - angle in △ABC. Let's assume we want to use the angle - sum property in △ABC. However, we can also use the fact that for similar triangles, corresponding angles are equal. Since we don't have enough information to pair up ∠A with a specific angle in △DEF directly from the problem setup, we note that in △DEF, we know ∠F = 67°.

Step3: Find ∠D in △DEF

Let's assume ∠A corresponds to ∠D (by the nature of similar triangles). Since the sum of angles in a triangle is 180° in △DEF, and we know ∠F = 67°. Let ∠D = 82° (assuming ∠A and ∠D are corresponding angles as they are in similar triangles). Then ∠E=180°-(82° + 67°)=31°.

Step4: Find ∠G

∠G is an exterior angle of △DEF. By the exterior - angle property of a triangle, an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So ∠G=∠D + ∠F. ∠G = 82°+67° = 149°.

Answer:

m∠E = 31°
m∠G = 149°