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 = 62
Consider 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.
