Question

Find the measure of angle PQR

Help me please

Answer 1

Given that the
`\widehat{PR}}=131^(\circ)`

We need to determine the measure of ∠PQR

Measure of ∠PQR:

The measure of ∠PQR can be determined using the formula,

`m \angle PQR=(1)/(2)(\widehat{PSR}-\widehat{PR})`

The measure of the arc PSR can be determined by subtracting the arc PR with 360°

Thus, we have;

`\widehat{PSR}=360^(\circ)-131^(\circ)=229^(\circ)`

Now, Substituting
`\widehat{PSR}=229^(\circ)`,
`\widehat{PR}}=131^(\circ)` in the formula, we have;

`m \angle PQR=(1)/(2)(229-131)`

`m \angle PQR=(1)/(2)(98)`

`m \angle PQR=49^(\circ)`

Thus, the measure of ∠PQR is 49°