Answer :
Final answer:
The measure of angle MAR is 28 degrees, obtained by setting up an equation using the properties of a bisected angle and solving for x, then substituting it back into the expression for the measure of angle RAT. Therefore the correct option is B
Explanation:
The student is asking about finding the measure of an angle when an angle is bisected. In this case, angle MAT is bisected by ray RAT, meaning that angles MAR and RAT are equal. Given that the measure of angle MAT is (6x - 4) degrees and the measure of angle RAT is (2x + 8) degrees, we can use the property that a bisected angle creates two equal angles to set up the equation (6x - 4) = 2(2x + 8).
Simplifying, we find 6x - 4 = 4x + 16, and by rearranging and solving for x, we get x = 10. Now, we substitute x back into the expression for the measure of angle RAT to get (2*10 + 8) degrees, which is 28 degrees. Hence, the measure of angle MAR is 28 degrees, which corresponds to option B.
