Find the value of X and Y in the parallelogram ### Directions: Find the value of X and Y in the parallelogram below. Show your calculations and equations.#### Diagram:- The shape in the diagram is a parallelogram.- There are four angles, and two of them are labeled with expressions: - \( (4x - 37)^\circ \) - \( 49^\circ \) - \( 4x - 3 \) - \( \frac{y}{5} \)#### Solution:1. **Understanding the properties of a parallelogram:** - Opposite angles in a parallelogram are equal. - Adjacent angles in a parallelogram are supplementary (sum to \(180^\circ\)).2. **Step-by-step calculations:** **Finding X:** - Consider the angles \( 4x - 3 \) and \( (4x - 37)^\circ \). - They must be equal because they are opposite angles in a parallelogram. \[ 4x - 3 = (4x - 37) \] - Solving for \( x \): \[ 4x - 3 = 4x - 37 \] \[ -3 = -37 \] This indicates an error, as both angles \( 4x - 3 \) and \( 4x - 37 \) contradict the property of equal opposite angles. **Alternative Approach:** - Consider the angle \( (4x - 37)^\circ \) and adjacent angle \( 49^\circ \). - These two angles must add up to \( 180^\circ \) (supplementary angles). \[ (4x - 37)^\circ + 49^\circ = 180^\circ \] \[ 4x - 37 + 49 = 180 \] \[ 4x + 12 = 180 \] \[ 4x = 168 \] \[ x = 42 \]3. **Finding Y:** - The angle opposite \( 49^\circ \) is \( \frac{y}{5} \). \[ \frac{y}{5} = 49

Name: Find the value of X and Y in the parallelogram ### Directions: Find th
Uploaded: 2024-03-20T06:47:08.000Z
Channel: Bartleby
Description: Find the value of X and Y in the parallelogram ### Directions: Find the value of X and Y in the parallelogram below. Show your calculations and equations.#### Diagram:- The shape in the diagram is a parallelogram.- There are four angles, and two of t