Question

1. solve for x.

a. ( x = 129 ) b. ( x = 30 )
c. ( x = 120 ) d. ( x = 40 )

Explanation:

Step1: Use the exterior - angle theorem

The exterior - angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles.
In \(\triangle PQR\), the exterior angle \(\angle PRS=(3x + 9)^{\circ}\), and the two non - adjacent interior angles are \(\angle P = 49^{\circ}\) and \(\angle Q=80^{\circ}\). So, \(3x + 9=49 + 80\).

Step2: Simplify the right - hand side of the equation

First, calculate \(49+80\).
\(49 + 80=129\), so the equation becomes \(3x+9 = 129\).

Step3: Solve for \(x\)

Subtract 9 from both sides of the equation:
\(3x+9-9=129 - 9\), which simplifies to \(3x=120\).
Then divide both sides by 3: \(x=\frac{120}{3}\).

Answer:

\(x = 40\) is incorrect.
\(x = 129\) is incorrect.
\(x = 120\) is incorrect.
\(x = 30\) is incorrect.
Wait, let's re - check:
From \(3x+9=49 + 80\) (exterior - angle theorem).
\(3x+9=129\)
Subtract 9: \(3x=129 - 9=120\)
Divide by 3: \(x = 40\). There was a miscalculation in the previous "Answer" part.
The correct answer is \(x = 40\), so the answer is D.