Question

Upper Delta ABC congruent Upper Delta DEF. Find the measure of the given angles.
m angle Upper Aequalsx plus 36
m angle Upper Dequals2 x

Answer 1

Since triangles \( \Delta ABC \) and \( \Delta DEF \) are congruent, their corresponding angles are equal. Thus, we can set up the equation:

\[
m \angle A = m \angle D
\]

Substituting the given expressions for the angles, we have:

\[
x + 36 = 2x
\]

Now, we can solve for \( x \) by isolating it on one side of the equation:

\[
x + 36 = 2x
\]
\[
36 = 2x - x
\]
\[
36 = x
\]

Now that we have \( x \), we can find the measure of \( m \angle A \) and \( m \angle D \):

\[
m \angle A = x + 36 = 36 + 36 = 72
\]

\[
m \angle D = 2x = 2(36) = 72
\]

Therefore, the measures of the angles are:

\[
m \angle A = 72^\circ \quad \text{and} \quad m \angle D = 72^\circ
\]

This confirms that both angles are equal, as expected in congruent triangles.