Question
The vertical angle of an isosceles triangle is 100º. Find its base angles.
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Answer
Consider an isosceles $\triangle\text{ABC}$ such that $\text{AB}=\text{AC}$ Given that vertical angle A is 100º To find the base angles Since $\triangle\text{ABC}$ is isosceles$\angle\text{B}=\angle\text{C}$ [Angles opposite to equal sides are equal]
And also, Sum of interior angles of a triangle = 180°$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
$(10)0^\circ+\angle\text{B}\angle\text{B}=180^\circ$
$2\angle\text{B}=180^\circ-(10)0^\circ$
$\angle\text{B}=40^\circ$
$\angle\text{B}=\angle\text{C}=40^\circ$
And also, Sum of interior angles of a triangle = 180°$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
$(10)0^\circ+\angle\text{B}\angle\text{B}=180^\circ$
$2\angle\text{B}=180^\circ-(10)0^\circ$
$\angle\text{B}=40^\circ$
$\angle\text{B}=\angle\text{C}=40^\circ$
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