Question

What is m∠A ? Enter your answer in the box. ° The figure shows what appears to be obtuse triangle A B C with obtuse angle A. The measure of angle A is left parentheses 3 times x plus 13 right parentheses degrees. The measure of angle B is left parentheses x minus 8 right parentheses degrees. The measure of angle C is x degrees.

Answer 1

The measure of angle A is 118°

Explanation:

Given: The figure shows an obtuse triangle ABC with obtuse angle A. The measure of angle A is ( 3x+ 13) degrees. The measure of angle B is(x - 8 ) degrees. The measure of angle C is x degrees.

We have to find the measure of angle A that is m ∠A.

ANGLE SUM PROPERTY OF A TRIANGLE states that in a triangle the sum of angles is always 180°

Given:

∠A = ( 3x + 13)°

∠B = ( x - 8)°

∠C = x°

Thus, applying angle sum property

∠A + ∠B + ∠C = 180°

Substitute, we get,

( 3x + 13)° + (x - 8)° + (x)° = 180°

Solving for x, we get,

3x + x + x + 5 = 180

5x = 175

Divide both side by 5, we get,

x = 35°

Thus, ∠A = ( 3x + 13)° = 118°

∠B = ( x - 8)° = 27°

∠C = x° = 35°

Thus, The measure of angle A is 118°