Exercise 34 Page 431

Find m∠ MSR using the fact that ∠ VSR and ∠ MSR form a linear pair.

SM< MR

Practice makes perfect

In order to determine the relationship between SM and MR, we can use Theorem 5.10 about Angle-Side Relationships in Triangles.

Angle-Side Relationships in Triangles
If one angle of a triangle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle.

With that being understood, let's now take a closer look at the given diagram.

We can see that ∠ MSR is opposite to MR and ∠ MRS is opposite to SM. However, the diagram does not show a measure for ∠ MSR. To find this measure, notice that ∠ VSM and ∠ MSR form a linear pair. The sum of their measures is 180^(∘). m∠ VSM + m∠ MSR =180^(∘) From the diagram, we know that ∠ VSM measures 110^(∘). Let's substitute this value into this equation and calculate the measure of ∠ MSR.

m∠ VSM + m∠ MSR =180^(∘)

Substitute

m∠ VSM= 110^(∘)

110^(∘) + m∠ MSR =180^(∘)

SubEqn

LHS-110^(∘)=RHS-110^(∘)

m∠ MSR =70^(∘)

We can add this piece of information to the diagram.

Because ∠ MSR is greater than ∠ MRS, we know that MR is longer than SM. SM< MR

Subchapter links

Exercises p.430-433

Exercise 34 Page 431

Hints

Check the answer

Practice exercises

Asses your skill