Measures: m∠1=90, m∠2=26, and m∠3=64 Theorems: Supplement Theorem and Complement Theorem
Practice makes perfect
Since ∠1 is a right angle, we know m∠1=90. Now, let's add some labels to the given diagram.
We can see that ∠1 and ∠ABD form a linear pair. Therefore, the Supplement Theorem gives us the following relation.
m∠1 + m∠ABD = 180
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, by using the Complement Theorem, we can say that ∠2 and ∠3 are complementary angles.
m∠2 + m∠3 = 90
To find the measure of m∠3, we substitute m∠2= 26 into the equation above and solve it.
