Question

Triangle abc has the following angle measures: m∠a = (x + 4)°, m∠b = (2x - 11)°, m∠c = (3x + 25)°. What is the measure of angle b?

1) 27°
2) 33°
3) 43°
4) 55°

Answer 1

The measure of angle b in triangle abc is found by using the triangle angle sum theorem, solving for x, and substituting back into the expression for m∠b. The correct measure of angle b is 43 degrees.

Step-by-step explanation:

The question asks for the measure of angle b in triangle abc with given angle measures m∠a, m∠b, and m∠c as algebraic expressions in terms of x. To find the measure of angle b, we can use the fact that the sum of angles in a triangle is 180 degrees.

First, we write the equation:

(x + 4)° + (2x - 11)° + (3x + 25)° = 180°

This simplifies to:

6x + 18 = 180

Solving for x:

x = (180 - 18) / 6

x = 27

Now we substitute x back into the expression for m∠b:

m∠b = (2x - 11)°

m∠b = (2(27) - 11)°

m∠b = (54 - 11)°

m∠b = 43°

Therefore, the measure of angle b is 43 degrees.