Question

ray at bisects ∠mar. if m∠mat=(8x - 3)° and m∠rat=(2x + 9)°, what is m∠mar?

Explanation:

Step1: Use angle - bisector property

Since ray AT bisects ∠MAR, then m∠MAT = m∠RAT. So we set up the equation 8x−3 = 2x + 9.

Step2: Solve the equation for x

Subtract 2x from both sides: 8x−2x−3=2x−2x + 9, which simplifies to 6x−3 = 9. Then add 3 to both sides: 6x−3 + 3=9 + 3, getting 6x = 12. Divide both sides by 6: $\frac{6x}{6}=\frac{12}{6}$, so x = 2.

Step3: Find m∠MAT or m∠RAT

Substitute x = 2 into the expression for m∠MAT (we could also use the expression for m∠RAT). m∠MAT=8x−3=8×2−3=16 - 3=13°.

Step4: Find m∠MAR

Since m∠MAR=m∠MAT + m∠RAT and m∠MAT = m∠RAT, then m∠MAR = 2×m∠MAT. So m∠MAR=2×13° = 26°.

Answer:

26°