Angle Pairs Unit Test

Question

15 of 1515 of 15 Items

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

Answer 1

m∠A + m∠B = 180°
22° + m∠B = 180°
m∠B = 180° - 22°
m∠B = 158°

m∠B + m∠C = 90°
158° + m∠C = 90°
m∠C = 90° - 158°
m∠C = -68°

Therefore, the equation to solve for m∠C is m∠C = -68°.

Answer 2

with more words please

Answer 3

Given that ∠A and ∠B are vertical angles, we know that they are congruent. We also know that ∠B is a complementary angle with ∠C, meaning that the sum of the measures of ∠B and ∠C is 90°.

Since ∠A and ∠B are vertical angles, we have:
m∠A + m∠B = 180°
Substitute the given measure m∠A=22° into the equation:
22° + m∠B = 180°
Solving for m∠B, we get:
m∠B = 180° - 22°
m∠B = 158°

Next, we use the fact that ∠B and ∠C are complementary angles:
m∠B + m∠C = 90°
Substitute the calculated measure of m∠B=158° into the equation:
158° + m∠C = 90°
Solving for m∠C, we get:
m∠C = 90° - 158°
m∠C = -68°

Therefore, the equation we can use to solve for m∠C, given m∠A=22°, is m∠C = -68°.

Answer 4

are you sure with this and can you make it shorter

Answer 5

I apologize for the error in my previous responses. Let me correct that and provide a shorter explanation.

Given:
1. ∠A = ∠B (Vertical angles)
2. ∠B + ∠C = 90° (Complementary angles)

Using the information above:
22° + m∠B = 180° (Vertical angles are supplementary)
m∠B = 180° - 22°
m∠B = 158°

158° + m∠C = 90° (Complementary angles)
m∠C = 90° - 158°
m∠C = -68°

Therefore, the equation to solve for m∠C is m∠C = -68°.

Answer 6

thanks

Answer 7

You're welcome! If you have any more questions or need further assistance, feel free to ask. Good luck with your studies!