Find the measure of angle∠A in the parallelogram to the right.

Question

Upper BB2 y degrees2y°3 y degrees3y°x degreesx°left parenthesis 4 x minus 180 right parenthesis degrees(4x−180)°
C
D
A


x y graph
Question content area bottom
Part 1
mangle∠Aequals=enter your response here
​(Type an integer or a decimal. Do not include

Answer 1

In a parallelogram, opposite angles are equal and adjacent angles are supplementary (i.e., they sum up to 180°).

From the information given, let's assume the following:

• Angle \( A = x \)
• Adjacent Angle \( B = 4x - 180 \)
• Opposite Angle \( C = x \)
• Opposite Angle \( D = 4x - 180 \)

Since angle \( A \) and angle \( B \) are adjacent, they must satisfy the following equation:

\[ A + B = 180° \]

Substituting in for angles \( A \) and \( B \):

\[ x + (4x - 180) = 180 \]

Now, solve for \( x \):

1. Combine like terms:

   \[ 5x - 180 = 180 \]

2. Add 180 to both sides:

   \[ 5x = 360 \]

3. Divide by 5:

   \[ x = 72 \]

Thus, the measure of angle \( \angle A \) is:

\[ \text{m}\angle A = 72° \]

So, the final answer is:

\[ \text{m}\angle A = 72 \]

(Type your answer as 72.)