Question

Given: \(_\text{ABC} = \_\text{DEF}\)

\(m \angle A = x + 38\)
\(m \angle D = 2x\)
To find: \(m \angle A\) and \(m \angle D\)
a) \(m \angle A = 38^\circ, m \angle D = 76^\circ\)
b) \(m \angle A = 40^\circ, m \angle D = 80^\circ\)
c) \(m \angle A = 76^\circ, m \angle D = 152^\circ\)
d) \(m \angle A = 114^\circ, m \angle D = 228^\circ\)

Answer 1

To find the measures of angles A and D, we can set up an equation using the fact that the corresponding angles in congruent triangles are equal. The measures of angles A and D are both 76°.

Step-by-step explanation:

To find the measures of angles A and D, we can set up an equation using the fact that the corresponding angles in congruent triangles are equal. Since ∠ABC is congruent to ∠DEF, we can write:

x + 38 = 2x

Simplifying the equation, we have:

x = 38

Substituting x back into the angle measures:

∠A = 38 + 38 = 76°

∠D = 2(38) = 76°

The measures of angles A and D are both 76°.