in a diagram angle a and angle b are vertical angles, and angel b is a complementary angle with angle c. if angle a=22, write an equation that you can use to solve for angle c.
Vertical angles are equal, so we know that angle a = angle b. We also know that angle b + angle c = 90 degrees (complementary angles add up to 90 degrees).
So, we have two equations:
1. angle a = angle b
2. angle b + angle c = 90
Substitute angle a = 22 into equation 1:
22 = angle b
Now substitute 22 for angle b in equation 2:
22 + angle c = 90
Subtract 22 from both sides to solve for angle c:
angle c = 90 - 22
angle c = 68
Therefore, angle c is equal to 68 degrees.