Question

Can anyone help? This is super difficult.

Answer 1

A is the correct answer :)

Answer 2

A

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:

`\displaystyle m\angle QPT = m\angle HQP + m\angle PHQ`

We are given the expressions of each angle. Substitute:

`(6x+20)^\circ = (x+40)^\circ + (4x-5)^\circ`

Solve for x:

`\displaystyle \begin{aligned} 6x + 20 & = (x+40) + (4x-5) \\ \\ 6x + 20 & = 5x + 35 \\ \\ x & = 15 \end{aligned}`

Hence, the value of x is 15.

Then the measure of ∠QPT will be:

`\displaystyle\begin{aligned} m\angle QPT & = (6x+20)^\circ \\ \\ & = (6(15)+20)^\circ \\ \\ & = (90 +20)^\circ \\ \\ & = 110^\circ\end{aligned}`

In conclusion, our answer is A.