Measures: m∠1 = 45, m∠3 = 62, and m∠4 = 45 Theorems: Complement and Supplement Theorems
Practice makes perfect
We are trying to find the measure of all of the angles. To begin, let's consider that since ∠2 and ∠3 are complementary, by using the Complement Theorem we can write the following equation.
m∠2+m∠3=90
Additionally, we are told that m∠2=28. By substituting that measure into the equation we just wrote, we can solve for m∠3.
28+m∠3=90 ⇒ m∠3 = 62Consider what other information we already know. It is said that ∠1≅ ∠4. Let's update the given diagram with the information we just found.
By analyzing the diagram, it can be seen that ∠AOB and ∠BOC are supplementary. Therefore, by using the Supplement Theorem, we can write the following equation.
m∠AOB + m∠BOC = 180
Now, using the Angle Addition Postulate we can rewrite m∠AOB and m∠BOC as the sum of two smaller angles.
m∠AOB &= m∠1 + 28
m∠BOC &= 62 + m∠4
Substituting these two expression into the equation derived from the Supplement Theorem, we will be able to find m∠1, which is equal to m∠4.
