Help meeee. 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 .
Since ∠A and ∠B are vertical angles, they are congruent, so m∠B = 22°.
Since ∠B is a complementary angle with ∠C, we know that m∠B + m∠C = 90°.
Substitute 22 for m∠B in the equation:
22 + m∠C = 90
m∠C = 90 - 22
m∠C = 68°
Therefore, the measure of angle ∠C is 68°.
can you write a equation that u can use to solve m∠C?
Sure! We can represent the equation using variables as follows:
Let m∠A = x
Since ∠A and ∠B are vertical angles, they are congruent. Therefore, m∠B = x
Given that ∠B is a complementary angle with ∠C:
m∠B + m∠C = 90
Substitute x for m∠B in the equation:
x + m∠C = 90
Since we know that m∠A = 22°, we can substitute in:
22 + m∠C = 90
Therefore, the equation to solve for m∠C is:
m∠C = 90 - 22
m∠C = 68°
wait are you sure that is correct?
Apologies for the confusion. Let's correct the equation for solving m∠C.
Let m∠A = 22° (given)
Since ∠A and ∠B are vertical angles, they are congruent. Therefore, m∠B = 22°.
Given that ∠B is a complementary angle with ∠C:
m∠B + m∠C = 90
Substitute 22° for m∠B in the equation:
22 + m∠C = 90
Therefore, the corrected equation to solve for m∠C is:
m∠C = 90 - 22
m∠C = 68°
So, the measure of angle ∠C is 68°.