Question

The vertex angle of an isosceles triangle measures 64 degrees. What is the measure of its base angles?

Answer 1

so hmmm check the picture below

in an isosceles triangle, two sides are equal, and thus the angles those twin legs make, are also twin angles

let's say the angle made is "a", so all internal angles will be 64 + a + a = 180
or 64 + 2a = 180

thus 2a = 180 - 64 => 2a = 116, thus a = 116/2

Answer 2

The measure of the base angle of an isosceles triangle is 58°.

What is an isosceles triangle?

"It is a triangle in which all three angles are less than 90°, and at least two of its angles are equal."

For given example,

The vertex angle of an isosceles triangle measures 64 degrees.

We know, for an isosceles triangle two base angles are of equal measures.

Let ∠x and ∠y are base angles of an isosceles triangle.

⇒ ∠x = ∠y

We know, the sum of all angles of the triangle is 180°.

⇒ ∠x + ∠y + 64 = 1 80

⇒ ∠x + ∠x = 180 - 64                              .....................(Since, ∠x = ∠y)

⇒ 2(∠x) = 116

⇒ ∠x = 116/2

⇒ ∠x = 58°

⇒ ∠y = 58°

Therefore, the measure of the base angle of isosceles triangle is 58°.

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