Measures: m∠ 2=m∠ 5=75 and m∠ 3=105. Theorem: Supplement Theorem.
Practice makes perfect
We are told that ∠ 2 and ∠ 4, as well as ∠ 4 and ∠ 5, are supplementary. Let's highlight these angles in the given diagram.
Using the Supplement Theorem, we get the following equations.
m∠ 2 + m∠ 4 &= 180
m∠ 4 + m∠ 5 &= 180
Additionally, we know that m∠ 4=105. By substituting it into the equations above we will find m∠ 2 and m∠ 5.
m∠ 2 + 105 &= 180 &⇒ m∠ 2 &= 75
105 + m∠ 5 &= 180 &⇒ m∠ 5 &= 75
No, we just need to find m∠ 3. To do so, we see from the diagram that ∠ 2 and ∠ 3 are also supplementary. Hence, the Supplement Theorem gives us the equation below.
m∠ 2 + m∠ 3 = 180
Substituting m∠ 2=75 above, we will get the measure of ∠ 3.
75 + m∠ 3 = 180 ⇒ m∠ 3 = 105
