∠C
 and ​∠D
​ are vertical angles with m∠C=−3x+58
 and m∠D=x−2
.

 

What is m∠D
?

Vertical angles are congruent, meaning they have equal measures. Therefore, the measures of ∠C and ∠D are the same.

We are given:
- m∠C = −3x + 58
- m∠D = x − 2

Since ∠C = ∠D, we can set up the equation:
\[
-3x + 58 = x - 2
\]

Now, solve for \( x \):

1. Add \( 3x \) to both sides:
\[
58 = 4x - 2
\]

2. Add 2 to both sides:
\[
60 = 4x
\]

3. Divide by 4:
\[
x = 15
\]

Now substitute \( x = 15 \) into the expression for \( m∠D \):
\[
m∠D = x - 2 = 15 - 2 = 13
\]

Thus, \( m∠D = 13^\circ \).

Would you like more details or have any questions?

Here are 5 related questions to explore:

1. What are the properties of vertical angles?
2. Can vertical angles ever be supplementary?
3. How would the problem change if m∠C = m∠D but both were negative?
4. What is the sum of two vertical angles?
5. How can you solve for x if m∠C = 90° and m∠D = x + 10?

**Tip:** When solving for unknowns in geometric equations, always look for congruent angles and apply their properties!

∠C and ∠D are vertical angles with m∠C = −3x + 58 and m∠D = x − 2. What is m∠D?

Learn how to solve for vertical angles in this step-by-step example where m∠C = −3x + 58 and m∠D = x − 2. Explore the use of algebraic equations and the vertical angles theorem. Suitable for students in Grades 8-10.

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