In isosceles triangle ABC, BC is the shortest side. If the degree measure of A is a multiple of 10, what is the smallest degree possible measure of B.

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06-12-2019
Mathematics

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In isosceles triangle ABC, BC is the shortest side. If the degree measure of A is a multiple of 10, what is the smallest degree possible measure of B.

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06-12-2019

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keshavgandhi04 keshavgandhi04 · Answer 2 · 2022-08-18T09:18:34-04:00

The smallest possible angle of B will be 5°.

What is a triangle?

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

There are many types of triangles such that right angle triangle, equilateral triangle, and much more.

Given ABC is an isosceles triangle and the shortest side in BC

So,

AB = AC

Now since angle A is a multiple of 10 so let's say it is 10x where x = 1,2,3,,.

Now the angle of B and C will be the same (y) by property of the isosceles triangle.

Now

The Sum of all angles will be

10x + y + y ≤ 180°

10x + 2y ≤ 180°

y ≤ 90° - 5x

Now if we take x = 18 than

y ≤ 0 which is a straight line

So, to make it a triangle we have to take x = 17

So,

y ≤ 90° - 5(17)

y ≤ 5°

Hence, The smallest possible angle of B will be 5°.

For more about triangles,

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