Question

triangle abc is similar to triangle def. angle a measures 28°, and angle b measures 74°. if angle f is the largest angle in triangle def, what is the measure of angle f? type the answer in the box.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In triangle ABC, we know ∠A = 28° and ∠B=74°. So, we first find ∠C in triangle ABC.
Let ∠C in triangle ABC be \(x\). Then \(x + 28^{\circ}+74^{\circ}=180^{\circ}\).

Step2: Calculate ∠C in triangle ABC

\(x=180^{\circ}-(28^{\circ} + 74^{\circ})=180^{\circ}-102^{\circ}=78^{\circ}\).

Step3: Use the property of similar triangles

Since \(\triangle ABC\sim\triangle DEF\), corresponding angles are equal. The largest angle in \(\triangle ABC\) is ∠C = 78°. The largest angle in \(\triangle DEF\) is ∠F. So, ∠F = 78°.

Answer:

78