In the accompanying figure, ABCD is a
parallelogram, mZA = 2x + 35, and mLC = 5x-22.
Find the value of x.
C
A
D
(5r-22)
(2x+35)
B



Answer :

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 \( 19 \).