Question

In triangle ABC, the measure of angle B is 50 degrees. Select all possible values for the measures of A and C if ABC is an acute triangle. m\angle∠A= 58 degrees; m\angle∠C= 72 degrees m\angle∠A= 100 degrees; m\angle∠C= 30 degrees m\angle∠A= 80 degrees; m\angle∠C= 50 degrees m\angle∠A= 60 degrees; m\angle∠C= 70 degrees m\angle∠A= 90 degrees; m\angle∠C= 40 degrees m\angle∠A= 105 degrees; m\angle∠C= 25 degrees

Answer 1

Answer:

Step-by-step explanation:

Sum of angle in a triangle = 180°

<A+<B+<C = 180

Given <B = 50°

Substituting into the formula

<A+50+<C = 180

<A+<C = 180-50

<A+<C = 130°

Since the ∆ABC is an acute triangle, the angles <A and <C must be angles less than 90° since acute angles are angles less than 90°

The possible values of <A and <C that will be acute and give a sum of 130° are;

∠A= 58° and ∠C= 72°

∠A= 80° and ∠C= 50°

∠A= 60° and ∠C= 70°

You can see that all the Angles are less than 90° and their sum is 130°