Given that ray AT bisects angle MAR, the measure of angle MAR is 38°.
Hence, option D)38° is the correct answer.
<h3>What is the m∠MAR?</h3>
Given the data in the question;
- Ray AT bisects ∠MAR
- m∠MAT = (4x − 5)°
- m∠RAT = (2x + 7)°
- m∠MAR = ?
Since ray AT bisects ∠MAR, both angle MAT and RAT are equal angles.
Hence,
m∠MAT = m∠RAT
(4x − 5) = (2x + 7)
We solve for x
4x − 5 = 2x + 7
4x - 2x = 7 + 5
2x = 12
x = 12/2
x = 6
Next, we find the numerical value of m∠MAT and m∠RAT.
m∠MAT = (4x − 5)
m∠MAT= 4(6) - 5
m∠MAT= 24 - 5
m∠MAT= 19°
m∠RAT = (2x + 7)
m∠RAT = 2(6) + 7
m∠RAT = 12 + 7
m∠RAT = 19°
m∠MAR = m∠MAT + m∠RAT
m∠MAR = 19° + 19°
m∠MAR = 38°
Given that ray AT bisects angle MAR, the measure of angle MAR is 38°.
Hence, option D)38° is the correct answer.
Learn more about angle bisector here: brainly.com/question/17111127
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