Question

5. In ΔA B C, if A C ≅ C B, m ∠A=3 x+18, m ∠ B=7 x- 58 , and m ∠C=2 x-8, find the measure of each angle.

x=____
m∠ A= ___
m∠ B= ___
m∠ C=___

Answer 1

`AC \cong BC \implies \angle A \cong \angle B \\ \\ \therefore m\angle A=m\angle B \implies 3x+18=7x-58 \\ \\ \implies 18=4x-58 \\ \\ 76=4x \\ \\ \boxed{x=19} \\ \\ m\angle A=3(19)+18 \implies \boxed{m\angle A=75^(\circ)} \\ \\ m\angle A=m\angle B \implies \boxed{m\angle B=75^(\circ)} \\ \\ m\angle C=180^(\circ)-m\angle A-m\angle B \implies \boxed{m\angle C=30^(\circ)}`