Question

Suppose that ABC is isosceles with base BA.Suppose also that mZ B=(5x+24)° and mC = (2x + 72).Find the degree measure of each angle in the triangle.с(2x + 72)m 2A =0D9Хm ZB =Аm LC =BT(5x + 24)口。

Answer 1

`m\angle A=49^(\circ),m\angle B=49^(\circ),m\angle C=82^(\circ)`

1) The best way to tackle questions like these is to sketch out:

2) We were told that this is an isosceles triangle therefore at least 2 of their angles are congruent to themselves. Therefore we can write down the following equation also considering the Triangle Sum Theorem:

`\begin{gathered} 5x+24+5x+24+2x+72=180 \\ 12x+48+72=180 \\ 12x+120=180 \\ 12x+120-120=180-120 \\ 12x=60 \\ (12x)/(12)=(60)/(12) \\ x=5 \end{gathered}`

Note that now, we can find the measure of each angle by plugging x=5:

`\begin{gathered} m\angle A=m\angle B=5x+24=5(5)+24=49^(\circ) \\ m\angle A=m\angle B=49^(\circ) \\ m\angle C=2(5)+72 \\ m\angle C=82^(\circ) \end{gathered}`

3) Thus the answer is:

`m\angle A=49^(\circ),m\angle B=49^(\circ),m\angle C=82^(\circ)`