Answer:
Explanation:
It's great that you included a diagram! It helps make the question more clear.
To find the measure of angle X, we will use the fact that the sum of the angles in a quadrilateral is 360°.
We can see from the diagram that there are seven angles in the quadrilateral. We will denote the angles as a1, a2, a3, b1, b2, b3, and b4, such that angle a1 is the angle at the top left of the quadrilateral, and angle b4 is the angle at the bottom right.
We can use the given angles to find the measures of some of the other angles in the quadrilateral. For example
32° + 142° + b4 = 180°
b4 = 180° - 32° - 142° = 46°
We can apply similar reasoning to find the measures of angles a2 and a3.
a1 + b2 = 180°
b2 = 180° - a1
a2 + b3 = 180°
b3 = 180° - a2
We now have enough information to find the measure of angle X.
The quadrilateral is symmetrical across the midline, so the measure of angle a3 must be equal to the measure of angle a1.
Now we can find the measure of angle X using the fact that the sum of the angles in a quadrilateral is 360°, and we have the measures of six of the seven angles.
a1 + a2 + a3 + b1 + b2 + b3 + b4 = 360°
a1 + 2a2 + b1 + b2 = 180°
We can use substitution to find the measure of angle X:
a3 + 2a2 + b1 + b2 = 180°
a3 = 180° - 2a2 - b1 - b2
Substituting this into the last equation, we get:
(180° - 2a2 - b1 - b2) + 2a2 + b1 + b2 = 180°
180° = (180° - 2