Final answer:
The measure of angle ∠MAR is 38°. This is determined by setting the equations for ∠MAT and ∠RAT equal, solving for x, and then doubling the resulting angle measure.
Step-by-step explanation:
The student is asking for the measure of the angle ∠MAR when given that ray AT bisects the angle. The measure of ∠MAT is given as (4x − 5)° and the measure of ∠RAT is given as (2x + 7)°. To solve for the measure of ∠MAR, we will set the two expressions equal to each other since AT bisects ∠MAR, meaning ∠MAT and ∠RAT are equal.
Step 1: Set the two expressions equal to find the value of x.
(4x − 5) = (2x + 7)
Step 2: Solve for x.
4x − 2x = 7 + 5
2x = 12
x = 6
Step 3: Find the measure of angle ∠MAR by plugging the value of x into either expression for ∠MAT or ∠RAT.
∠MAT = (4x − 5)° = (4(6) − 5)° = 24 − 5 = 19°
Since ∠MAT is equal to ∠RAT and they combine to form ∠MAR, the measure of angle ∠MAR is double ∠MAT:
m∠MAR = 2 × 19° = 38°
Therefore, the answer is (d) 38°.