Question

Triangle ABC is an isosceles triangle. Angles B and C are base angles, with measurements of (5x - 10)° and (4x + 5)°, respectively. What is m

15 °
35 °
50 °
60 °

Answer 1

`\bf{50 \degree }`

Explanation:

Given:

`\begin{aligned}&\sf \triangle \ ABC \\&\sf \angle B \ \cong \angle C \end{aligned}`

Solve for x

`\begin{aligned}&\sf 5x-10=4x+5 \\&\sf 5x-4x=5+10 \\&\sf x=15 \end{aligned}`

Solve for ∠B

`\begin{aligned}&\sf (5x-10)\degree \\=&\sf \ (5(15)-10)\degree \\=&\sf \ (75-10)\degree \\=&\sf \ 65 \degree \end{aligned}`

Solve for m

`\begin{aligned}&\sf m=180 \degree -(\angle B + \angle C) \\&\sf m=180 \degree -(65 \degree + 65 \degree ) \\&\sf m=180 \degree - 130 \degree \\&\boxed{\bf{m=50 \degree }} \end{aligned}`