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In an isosceles triangle, if the measure of a base angle is 74°, what is the measure of the vertex angle?

Answer 1

Mason Adams

The vertex angle would be #32^o#

In an isosceles triangle the base angles would be congruent and therefore both have measures of #74^o#

The three angles of any triangle must add up to #180^o#

Therefore

#74^o + 74^o + v = 180^o#
#148^o + v = 180^o#
#v = 32^o#

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Answer 2

Claire Akin

Since an isosceles triangle has two congruent base angles, if one base angle is 74°, then the other base angle is also 74°. The sum of the angles in any triangle is always 180°. Therefore, to find the measure of the vertex angle, subtract the sum of the base angles from 180°:

180° - (74° + 74°) = 180° - 148° = 32°

So, the measure of the vertex angle in the isosceles triangle is 32°.

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