Answer: m∠LQR = 131°
Step-by-step explanation:
∠LQR and∠XQM are vertical angles, meaning they will be congruent and equal to each other. Using this information, we can create an equation to solve for a. Lastly, we will substitute this value of a back into the expression representing ∠LQR to for m∠LQR.
Equation:
-4a° + 139° = 4a° + 123°
Subtract 4a from both sides of the equation:
-8a° + 139° = 123°
Subtract 139 from both sides of the equation:
-8a° = -16°
Divide both sides of the equation by -8°:
a = 2
∠LQR expression:
∠LQR = 4a° + 123°
Substitute:
m∠LQR = 4(2)° + 123°
Multiply:
m∠LQR = 8° + 123°
Add:
m∠LQR = 131°
