Question

4. If the measures of angles A and B of triangle

ABC are each 2x + 5 and the measure of angle
C is 3x – 5, what is the measure of angle exterior
to angle A?​

Answer 1

The measure of the exterior angle to angle A in triangle ABC is 70 degrees.

Step-by-step explanation:

The measure of the exterior angle to angle A can be found by subtracting the sum of angles A and B from 180 degrees. Given that the measure of angle A is 2x + 5 and the measure of angle B is also 2x + 5, we can set up the equation: (2x + 5) + (2x + 5) + (3x - 5) = 180. Simplifying this equation, we get 7x + 5 = 180. Solving for x, we find x = 25. Substituting this value back into the expression for angle A, we get: angle A = 2(25) + 5 = 55 degrees. Therefore, the measure of the exterior angle to angle A is 180 - (angle A + angle B) = 180 - (55 + 55) = 70 degrees.

Answer 2

5x

Step-by-step explanation:

. If the measures of angles A and B of triangle

ABC are each 2x + 5 and the measure of angle

C is 3x – 5, what is the measure of angle exterior

to angle A?​

Using the theorem

The sum of interior angle of a triangle is equal to its exterior

Given the interior angles 2x+5 and 3x-5

Sum= 2x+5+3x-5

Sum = 2x+3x+5-5

Sum = 5x+0

Sum = 5x

Hence the measure of the exterior angle is 5x