Question

Question 10
A) Two angles are supplementary with measures mQRS = (x+30)° and m✩SRT = (2x)°. What is the value of mQRS? (1 point)
180°
O 80°
100°
50°
Question 11
A) Four angles share a vertex. They have the following measures: m21 = 63°, m≤2 = 117°, m23 = 63°, and m24 = 117°. Which angle is a vertical angle with 22? (1 point)
24
O 41
OOO
none
23

Answer 1

For Question 10, we know that two angles are supplementary if their measures add up to 180°. The measures are given as:

- mQRS = (x + 30)°
- mSRT = (2x)°

Setting up the equation for supplementary angles:

\[
(x + 30) + (2x) = 180°
\]

Combining like terms:

\[
3x + 30 = 180
\]

Subtracting 30 from both sides:

\[
3x = 150
\]

Dividing by 3:

\[
x = 50
\]

Now substituting back to find mQRS:

\[
mQRS = (x + 30) = (50 + 30) = 80°
\]

So, the value of mQRS is **80°**.

---

For Question 11, we have four angles:

- m21 = 63°
- m22 = 117°
- m23 = 63°
- m24 = 117°

Vertical angles are formed by two intersecting lines and consist of pairs of angles that are opposite each other. Here, we need to find the angle that is vertical to angle m22 (measured at 117°).

The vertical angle to m22 (117°) is m24, which also measures 117°.

So the answer is angle **24**.