Question

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

Explanation:

Step1: Apply 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 \(\angle SRQ=58^{\circ}\).

Step2: Calculate \(x\)

By the exterior angle theorem, \(x = 35 + 58\).

$$x=93$$

Answer:

\(x = 93\)