Answer:
In the given problem, we have two angles:
∠ABM = 3x + 17
∠ABC = 125°
∠MBC = 5x + 20
We are asked to find the measure of angle ∠MBC.
According to the Angle Sum Property of a triangle, the sum of the angles in a triangle is always 180°.
∠ABM + ∠ABC + ∠MBC = 180°
Substitute the given angle measures:
(3x + 17) + 125 + (5x + 20) = 180
Combine like terms:
8x + 162 = 180
Now, solve for x:
8x = 180 - 162
8x = 18
x = 18 / 8
x = 2.25
Now that we have the value of x, we can find the measure of ∠MBC:
∠MBC = 5x + 20
∠MBC = 5 * 2.25 + 20
∠MBC = 11.25 + 20
∠MBC = 31.25°
Therefore, the measure of angle ∠MBC is 31.25 degrees.
Explanation: