Question

Triangle ABC is an isosceles triangle. Angles B and C are base angles, with measurements of (11x −10)° and (7x + 10)°, respectively. What is m∠A?5°90°85°35°

Answer 1

Given:

Triangle ABC is an isosceles triangle. Angles B and C are base angles, with measurements of

`\begin{gathered} \angle B=(11x-10)\degree \\ \angle C=(7x+10)\degree \end{gathered}`

Required:

To find the angle A.

Step-by-step explanation:

Triangle ABC is an isosceles triangle.

Therefore,

`\angle B=\angle C`
`\begin{gathered} 11x-10=7x+10 \\ 11x-7x=10+10 \\ 4x=20 \\ x=(20)/(4) \\ \\ x=5 \end{gathered}`

Now,

`\begin{gathered} \angle B=11(5)-10 \\ =55-10 \\ =45\degree \\ \\ \angle C=7(5)+10 \\ =35+10 \\ =45\degree \end{gathered}`

The angle A is,

`\begin{gathered} \angle A+\angle B+\angle C=180 \\ \angle A=180-45-45 \\ \angle A=90\degree \end{gathered}`

Final Answer:

`\angle A=90\degree`