Exercise 9 Page 728

In the given diagram, we want to find the measure of the arc PQR.

Note that the minor arc PQR and the major arc PSR are adjacent arcs. By the Arc Addition Postulate, we know that the measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs. In this case, the arc formed by these two adjacent arcs is a full circle, which measures 360^(∘). m PQR+mPSR=360 First, we can find the measure of PSR using the Arc Addition Postulate. Since we know that mPT= 72, mTS= 75, and mSR= 90, we can write the equation for mPSR and substitute these values to solve it.

mPSR=mPT+mTS+mSR

SubstituteValues

Substitute values

mPSR= 72+ 75+ 90

AddTerms

Add terms

mPSR= 237

Now, remembering that the measures of arcs PQR and PSR add up to 360^(∘), we can substitute the obtained value into our first equation and solve for mPQR.

mPQR+mPSR=360

Substitute

mPSR= 237

mPQR+ 237=360

SubEqn

LHS-237=RHS-237

mPQR=123

We found that PQR measures 123^(∘).