Apply the angle addition postulate and some properties of equality to find the value of x
Let m Angle UQR = 11x +9°, m angle PQU= 100°, and m angle PQR= 31x+9°
To find the value of x, we will first use the Angle Addition Postulate, which states that the measure of the whole angle is equal to the sum of the measures of its two non-overlapping parts.
Therefore, we can set up an equation using the given angles:
m angle UQR = m angle PQU + m angle PQR
11x + 9 = 100 + 31x + 9
Next, we will combine like terms and simplify the equation:
11x + 9 = 31x + 109
10 = 20x
x = 10/20
x = 1/2
Therefore, the value of x is 1/2.