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
