One of the base angles of an isosceles triangle is equal to 45∘. Find the vertex angle of the triangle.
74∘
Let Δ ABC be the isosceles triangle with one of base angle 45∘ as shown below.
Here, vertex angle =∠A
By angle sum property, ∠A+∠B+∠C=180∘
In Isosceles triangle, base angles are equal. Hence two angles will be equal i.e ∠B=∠C=45∘
So, ∠A=180∘−(∠B+∠C)
= 180∘−(45∘+45∘)
= 180∘−90∘
= 90∘