Angle Pairs Unit Test
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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)
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°.
with more words please
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°.
are you sure with this and can you make it shorter
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°.