Question

what are the values of p and b? p = − b = −

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. Here, \(b=p + p\) (since \(b\) is an exterior angle and the two non - adjacent interior angles are both \(p\)). Also, we know that \(b=p + 34^{\circ}\) (given from the figure).

Step2: Solve for \(p\)

Set the two expressions for \(b\) equal to each other: \(2p=p + 34^{\circ}\). Subtract \(p\) from both sides: \(2p−p=p + 34^{\circ}-p\). So, \(p = 34^{\circ}\).

Step3: Solve for \(b\)

Substitute \(p = 34^{\circ}\) into the equation \(b=p + 34^{\circ}\). Then \(b=34^{\circ}+34^{\circ}=68^{\circ}\).

Answer:

\(p = 34\), \(b = 68\)