Question

Triangle ABC has the following angle measures:

m∠a = (x 4)°, m∠b = (2x − 11)°, m∠c = (3x 25)°. What is m∠b?
a. 27°
b. 33°
c. 43°
d. 55°

Answer 1

Upon setting up and solving the equation based on the sum of angles in a triangle being 180 degrees, we determine that the value of x is 27. Substituting this into the expression for m∠B, we find that m∠B is 43°.

Step-by-step explanation:

The student is asking to find m∠b for triangle ABC given the angle measures m∠A = (x + 4)°, m∠B = (2x − 11)°, and m∠C = (3x + 25)°. Since the sum of the angles in any triangle is 180 degrees, we can set up the following equation:

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

Solving for x, we get:

x + 4 + 2x - 11 + 3x + 25 = 180

6x + 18 = 180

6x = 162

x = 27

Now, substituting x back into m∠B:

m∠B = (2x − 11)

m∠B = (2*27 − 11)

m∠B = 54 - 11

m∠B = 43°.

Therefore, the measure of angle B, m∠b, is 43°.