Exercise 4 Page 508

We are asked to find the measure of ∠TSR using the given information. Let's notice that ∠PTQ and ∠STR are vertical angles, so they are congruent. This means that m∠STR= 67.

Since diagonals in a rectangle have the same lengths and bisect each other, ST=RT. This means that the triangle STR is isosceles and m∠TSR=m∠TRS.

Using the Triangle Sum Theorem we can find the measure of ∠TSR. Let's recall that according to this theorem, the sum of the measures of angles in a triangle is always 180. We will use the fact we found above that m∠TSR=m∠TRS.

m∠STR+m∠TSR+m∠TRS=180

SubstituteII

m∠STR= 67, m∠TRS= m∠TSR

67+m∠TSR+ m∠TSR=180

AddTerms

Add terms

67+2m∠TSR=180

SubEqn

LHS-67=RHS-67

2m∠TSR=113

DivEqn

.LHS /2.=.RHS /2.

m∠TSR=56.5

We found that the measure of ∠TSR is 56.5.