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Sagot :
Given:
Triangle ABC is an isosceles triangle. Angles B and C are base angles, with measurements of
[tex]\begin{gathered} \angle B=(11x-10)\degree \\ \angle C=(7x+10)\degree \end{gathered}[/tex]Required:
To find the angle A.
Explanation:
Triangle ABC is an isosceles triangle.
Therefore,
[tex]\angle B=\angle C[/tex][tex]\begin{gathered} 11x-10=7x+10 \\ 11x-7x=10+10 \\ 4x=20 \\ x=\frac{20}{4} \\ \\ x=5 \end{gathered}[/tex]Now,
[tex]\begin{gathered} \angle B=11(5)-10 \\ =55-10 \\ =45\degree \\ \\ \angle C=7(5)+10 \\ =35+10 \\ =45\degree \end{gathered}[/tex]The angle A is,
[tex]\begin{gathered} \angle A+\angle B+\angle C=180 \\ \angle A=180-45-45 \\ \angle A=90\degree \end{gathered}[/tex]Final Answer:
[tex]\angle A=90\degree[/tex]
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