Measures: m∠ 1=90, m∠ 2=53, and m∠ 3=37 Theorems: Supplement Theorem and Complement Theorem
Practice makes perfect
Let's begin by adding some labels to the given diagram.
We can see that ∠ 1 and ∠ ABD form a linear pair. Therefore, by the Supplement Theorem, the sum of the measures of ∠ 1 and ∠ ABD needs to be equal to 180.
m∠ 1 + m∠ ABD = 180Since ∠ 1 is a right angle, we know that m∠ 1=90. Therefore, we can find m∠ ABD by substituting m∠ 1= 90 into this equation.
Now, since ∠ 2 and ∠ 3 are adjacent angles that form the right angle ∠ ABD, we can say that ∠ 2 and ∠ 3 are complementary angles. By the Complement Theorem, this means that the sum of their measures is equal to 90.
m∠ 2 + m∠ 3 = 90
Next, to find their measures, we can substitute m∠ 2= x and m∠ 3= x-16 into the equation above and solve it for x.
Finally we can use the value of x we found to calculate m∠ 2 and m∠ 3.
lll
m∠ 2=x & ⇒ & m∠ 2= 53
m∠ 3=x-16 & ⇒ & m∠ 3= 53-16
& & =37
The measure of ∠ 2 is 53 and the measure of ∠ 3 is 37.
