Answer:
m<C = 66°
Explanation:
Perpendicular bisector, AB divides angle CAD into two equal parts. Therefore:
(5x + 9)° = (7x + 3)°
Solve for x
5x + 9 = 7x + 3
Collect like terms
5x - 7x = -9 + 3
-2x = -6
Divide both sides by -2
x = 3
✔️m<C + m<CBA + m<BAC = 180° (sum of triangle)
m<C + 90° + (7x + 3)° = 180 (substitution)
Plug in the value of x and solve
m<C + 90 + 7(3) + 3 = 180
m<C + 90 + 21 + 3 = 180
m<C + 114 = 180
m<C = 180 - 114 (Subtraction property of equality)
m<C = 66°