Question

In a diagram, ∠A
∠
𝐴
and ∠B
∠
𝐵
are vertical angles, and ∠B
∠
𝐵
is a complementary angle with ∠C
∠
𝐶
. If m∠A=22°
𝑚
∠
𝐴
=
22
°
, write an equation that you can use to solve for m∠C
𝑚
∠
𝐶
.(2 points)
describe as a 7th grader and sort of simply

Answer 1

turn it all to text

Answer 2

To solve for the measure of angle \( C \), we can use the facts about the relationships between the angles given in the problem.

1. **Vertical Angles**: Angle \( A \) and angle \( B \) are vertical angles. This means they are equal, so:
\[
m∠A = m∠B
\]

2. **Complementary Angles**: Angle \( B \) and angle \( C \) are complementary angles. This means that when you add their measures together, they equal \( 90° \):
\[
m∠B + m∠C = 90°
\]

Now we know that \( m∠A = 22° \), so we can find \( m∠B \):
\[
m∠B = m∠A = 22°
\]

Now we can substitute \( m∠B \) into the complementary angle equation:
\[
22° + m∠C = 90°
\]

To solve for \( m∠C \), we can write the equation:
\[
m∠C = 90° - 22°
\]

This is the equation you can use to find the measure of angle \( C \). Now, you can just calculate the right side:
\[
m∠C = 68°
\]

So, to sum it up: the equation to use is \( m∠C = 90° - m∠B \), and by plugging in \( m∠B \), you find out that \( m∠C = 68° \).