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:

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°

Final answer:

Out of the options provided, for an acute triangle ABC with angle B equal to 50 degrees, angles A and C can measure 58 and 72 degrees respectively or 60 and 70 degrees.

Explanation:

In Mathematics, especially Geometry, we know that the sum of the angles in any triangle, acute or otherwise, equals 180 degrees. In the given triangle ABC, m∠B is 50 degrees. If ABC is an acute triangle, none of these angles can be equal to or more than 90 degrees as an acute angle is less than 90 degrees.

So the possible values for measures of angles A and C are:

• m∠A= 58 degrees; m∠C= 72 degrees
• m∠A= 60 degrees; m∠C= 70 degrees

The other options cannot be correct because either they would make the sum of the angles more than 180 degrees, or one of the angles would be equal to or greater than 90 degrees.

Learn more about Acute Triangle here:

brainly.com/question/36906867

#SPJ3