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

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.

68.2 degrees

Step-by-step 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.

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.