Here is your answer my dear frined
Step-by-step explanation:
To solve for \( x \) in a parallelogram where the measures of two angles \( \angle A \) and \( \angle C \) are given as \( 2x + 35 \) and \( 5x - 22 \) respectively, we use the properties of parallelograms.
In a parallelogram:
1. Opposite angles are equal.
2. The sum of the measures of any two adjacent angles is \( 180^\circ \).
Since \( \angle A \) and \( \angle C \) are opposite angles in the parallelogram, their measures are equal. Therefore:
\[
2x + 35 = 5x - 22
\]
To solve for \( x \), follow these steps:
1. **Isolate \( x \)**:
\[
2x + 35 = 5x - 22
\]
Subtract \( 2x \) from both sides:
\[
35 = 3x - 22
\]
Add 22 to both sides:
\[
57 = 3x
\]
Divide by 3:
\[
x = 19
\]
So, the value of \( x \) is \( 19 \).