Question

DEF is a translation of ABC. If m∠ A = 2x - 10° and m∠ D = 3x - 52°, how many degrees are contained in ∠A?**

A. m ∠A = 2x°

B. m ∠A = 2x - 10°

C. m ∠A = 3x - 52°

D. m ∠A = x - 21°

Answer 1

To find the measure of angle A, we set the angle expressions equal since triangle DEF is a translation of triangle ABC, meaning their corresponding angles are equal. Solving 2x - 10 = 3x - 52, we get x = 42. Substituting x into the expression for angle A gives m∠A = 74 degrees.

Step-by-step explanation:

We are given triangle DEF as a translation of triangle ABC, which means their corresponding angles are equal. The measures of angles A and D are related as a translation does not change the measure of angles. To find the measure of ∠A, we set the expressions for ∠A and ∠D equal to each other because they are corresponding angles and therefore equal:

m∠A = 2x - 10°

m∠D = 3x - 52°

Since ∠A is equal to ∠D, we have:

2x - 10 = 3x - 52

Adding 52 to both sides and subtracting 2x from both sides gives us:

x = 42

Substituting x back into the expression for m∠A, we get:

m∠A = 2x - 10 = 2(42) - 10 = 84 - 10 = 74°

Therefore, the measure of ∠A is 74 degrees.