Answer:
A
Step-by-step explanation:
Recall that from the Exterior Angle Theorem, the exterior angle is equal to the sum of the two interior angles opposite from the exterior angle.
In other words:
[tex]\displaystyle m\angle QPT = m\angle HQP + m\angle PHQ[/tex]
We are given the expressions of each angle. Substitute:
[tex](6x+20)^\circ = (x+40)^\circ + (4x-5)^\circ[/tex]
Solve for x:
[tex]\displaystyle \begin{aligned} 6x + 20 & = (x+40) + (4x-5) \\ \\ 6x + 20 & = 5x + 35 \\ \\ x & = 15 \end{aligned}[/tex]
Hence, the value of x is 15.
Then the measure of ∠QPT will be:
[tex]\displaystyle\begin{aligned} m\angle QPT & = (6x+20)^\circ \\ \\ & = (6(15)+20)^\circ \\ \\ & = (90 +20)^\circ \\ \\ & = 110^\circ\end{aligned}[/tex]
In conclusion, our answer is A.
