Question

An artist used a program to enlarge a triangular figure. The original is shown in the figure as △ABC and the enlargement is △DEF so △ABC∼△DEF.

Triangles ABC and DEF with measures as described in the problem.

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Given that m∠A≈68.2°, ∠C is a right angle, AC=2, BC=5, AB=29−−√, DE≈8.1, EF=7.5, and DF=3, what is the measure of ∠D?

m∠D=__________°

Enter your answer as the number that correctly fills in the blank, like this: 42

Answer 1

68.2 degrees

Explanation:

An artist used a program to enlarge a triangular figure. The original is shown in the figure as △ABC and the enlargement is △DEF so △ABC∼△DEF. Triangles ABC and DEF with measures as described in the problem. Given that m∠A≈68.2°, ∠C is a right angle, AC=2, BC=5, AB=29−−√, DE≈8.1, EF=7.5, and DF=3, the measure of ∠D is 68.2 degrees.

Answer 2

Looking at the order of the letters ABC and DEF

A = D

B = E

C = F

The triangle was enlarged so this would change the length of the sides but because the triangles are similar, the angles do not not change.

You are told angle A = 68.2 degrees, this would mean angle D is also 68.2 degrees.