Final answer:
By setting up an equation based on the sum of angles in a triangle, solving for x, and substituting back into the expression for angle B, we find that the measure of angle B is 43 degrees.
Step-by-step explanation:
The student's question pertains to finding the measure of angle B in a triangle with given algebraic expressions for the measures of its angles. To determine the value of angle B, we utilize the fact that the sum of the angles in any triangle is 180 degrees. We set up the equation (x + 4) + (2x - 11) + (3x + 25) = 180 and solve for x. Once we have the value of x, we substitute it back into the expression for m°B, which is (2x - 11), to find the measure of angle B.
Setting up the equation:
- (x + 4) + (2x - 11) + (3x + 25) = 180
- 6x + 18 = 180
- 6x = 162
- x = 27
Then, substituting into m°B:
- m°B = (2(27) - 11)
- m°B = 54 - 11
- m°B = 43 degrees
Therefore, the measure of angle B is 43 degrees.