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 . Make it look like an essay.
Answer
Make it shorter but still correct
Answered by GPT 3.5
In this diagram, we are given that ∠A and ∠B are vertical angles. Vertical angles are a pair of non-adjacent angles formed by two intersecting lines. These angles are always congruent, meaning they have the same measure. Thus, we can say that m∠A = m∠B.

Additionally, it is given that ∠B is a complementary angle with ∠C. Complementary angles are two angles whose measures add up to 90 degrees. Therefore, we can express this relationship as m∠B + m∠C = 90°.

Given that m∠A = 22°, we can substitute this value into the equation m∠A = m∠B to obtain 22° = m∠B. Substituting this value into the equation m∠B + m∠C = 90°, we have 22° + m∠C = 90°.

By rearranging this equation, we can solve for m∠C. Subtracting 22° from both sides gives us m∠C = 90° - 22°. Simplifying the right side of the equation, we get m∠C = 68°.

Therefore, the equation we can use to solve for m∠C is m∠C = 90° - 22°, which simplifies to m∠C = 68°.
Answered by GPT 3.5
Given that ∠A and ∠B are vertical angles, we know that they are congruent, so m∠A = m∠B.

It is also given that ∠B is a complementary angle with ∠C, meaning m∠B + m∠C = 90°.

Since m∠A = 22°, we can substitute this value into the equation m∠A = m∠B to obtain 22° = m∠B.

Substituting this value into the equation m∠B + m∠C = 90°, we have 22° + m∠C = 90°.

We can solve for m∠C by subtracting 22° from both sides, resulting in m∠C = 90° - 22°.

Simplifying the right side of the equation, we get m∠C = 68°.

Therefore, the equation we can use to solve for m∠C is m∠C = 90° - 22°, which simplifies to m∠C = 68°.