Question

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

1) 27°
2) 33°
3) 43°
4) 55°

Answer 1

To find the measure of angle ∠b, we need to determine the value of x and substitute it into the expression for ∠b. Substituting the value of x into the expression for ∠b, we get ∠b = (2(27) - 11)° = 43°. Therefore, the measure of ∠b is 43°.

Step-by-step explanation:

To find the measure of angle ∠b, we need to determine the value of x and substitute it into the expression for ∠b.

Given: ∠a = (x + 4)°, ∠b = (2x - 11)°, ∠c = (3x + 25)°

Since the sum of the angles in a triangle is 180°, we can write the equation: (∠a) + (∠b) + (∠c) = 180°.

Substituting the given values, we get: (x + 4) + (2x - 11) + (3x + 25) = 180.

Simplifying the equation: 6x + 18 = 180.

Subtracting 18 from both sides: 6x = 162.

Dividing by 6: x = 27.

Substituting the value of x into the expression for ∠b: ∠b = (2(27) - 11)° = 43°.

Therefore, the measure of ∠b is 43°.