Question

? the base angle of an isosceles triangle is 50. what is its vertex angle? a) cpctc b) 80 c) asa d) sss theor

Explanation:

Step1: Recall the property of isosceles triangle

In an isosceles triangle, the base angles are equal. Let the base angles be \( \angle B=\angle C = 50^{\circ}\)

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). Let the vertex angle be \(A\). Then \(A + B + C=180^{\circ}\)
Substitute \(B = C=50^{\circ}\) into the equation: \(A+50^{\circ}+50^{\circ}=180^{\circ}\)

Step3: Solve for the vertex angle \(A\)

\(A=180^{\circ}-(50^{\circ}+50^{\circ})\)
\(A = 180^{\circ}-100^{\circ}\)
\(A = 80^{\circ}\)

Answer:

\(80^{\circ}\)