Upper Delta ABC congruent Upper Delta DEF. Find the measure of the given angles.

Question

m angle Upper Aequalsx plus 27
m angle Upper Dequals2 x
Question content area bottom
Part 1
m angle Upper Aequals
  
enter your response heredegrees
​(Do not include the degree symbol in your​ answer.)
Part 2
m angle Upper Dequals
  
enter your response heredegrees
​(Do not include the degree symbol in your​ answer.)

Answer 1

Since triangles ABC and DEF are congruent, the measures of their corresponding angles are equal. Therefore, we have:

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

According to the problem, we are given:

\[ m \angle A = x + 27 \] \[ m \angle D = 2x \]

Setting these two expressions equal to each other since the angles are congruent:

\[ x + 27 = 2x \]

Now, we can solve for \(x\):

1. Subtract \(x\) from both sides: \[ 27 = 2x - x \] \[ 27 = x \]

2. Now that we have found \(x\), we can find the measure of angle A: \[ m \angle A = x + 27 = 27 + 27 = 54 \]

3. Also, we can find the measure of angle D: \[ m \angle D = 2x = 2 \times 27 = 54 \]

Thus, the final answers are:

Part 1: \[ m \angle A = 54 \]

Part 2: \[ m \angle D = 54 \]

(Note: Remember to enter the responses without the degree symbol, as instructed).