Question

for each part, just put the number. dont put x = # or a degree symbol or the word degree or the words, \i got...\ what is the value of x? what is the measure of the angle with the red arrow pointing at it? what is the measure of the angle with the blue arrow pointing at it?

Explanation:

Step1: Recall quadrilateral angle - sum

The sum of interior angles of a quadrilateral is 360°. One angle is 90°. So, \(x+(x - 50)+90+\text{fourth - angle}=360\).

Step2: Assume it's a trapezoid with parallel sides

If the two non - right angles are supplementary (for a trapezoid with one right angle and parallel sides), then \(x+(x - 50)=180\).

Step3: Solve the equation

\[

$$\begin{align*} x+(x - 50)&=180\\ 2x-50&=180\\ 2x&=180 + 50\\ 2x&=230\\ x&=115 \end{align*}$$

\]

Step4: Find the blue - arrowed angle

The angle with the blue arrow is \(x-50\). Substitute \(x = 115\) into \(x - 50\), we get \(115-50 = 65\).

Answer:

1. 115
2. 115
3. 65