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.
