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.
