Question

question 2 (multiple choice worth 4 points) (01.07r mc) ray at bisects ∠mar. if m∠mat=(6x - 4)° and m∠rat=(2x + 8)°, what is the m∠mar. 62° 28° 14° 3°

Explanation:

Step1: Set equal angles

Since ray AT bisects ∠MAR, then $m\angle MAT=m\angle RAT$. So we set up the equation $6x - 4=2x + 8$.

Step2: Solve for x

Subtract $2x$ from both sides: $6x-2x - 4=2x-2x + 8$, which simplifies to $4x-4 = 8$. Then add 4 to both sides: $4x-4 + 4=8 + 4$, getting $4x=12$. Divide both sides by 4: $x=\frac{12}{4}=3$.

Step3: Find $m\angle MAT$ or $m\angle RAT$

Substitute $x = 3$ into $m\angle MAT=6x - 4$. So $m\angle MAT=6\times3-4=18 - 4=14^{\circ}$.

Step4: Calculate $m\angle MAR$

Since $m\angle MAR=m\angle MAT + m\angle RAT$ and $m\angle MAT=m\angle RAT$, then $m\angle MAR = 2\times m\angle MAT$. So $m\angle MAR=2\times14^{\circ}=28^{\circ}$.

Answer:

$28^{\circ}$