Question

what is the value of x? art not to scale. x = 23 x = 35 x = 58 x = 93

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In triangle \(SQR\), \(\angle PQS\) (which is \(x^{\circ}\)) is an exterior angle. The two non - adjacent interior angles are \(\angle QSR = 35^{\circ}\) and \(\angle QRS=58^{\circ}\).
So, \(x = 35 + 58\)

Step2: Calculate the sum

\(x=35 + 58=93\)

Answer:

\(x = 93\) (the fourth option: \(x = 93\))