Let's find the measures of the numbered angles in the given parallelogram one at a time.
Measure of ∠ 2
Recall the theorem referenced in the book that states that if a quadrilateral is a parallelogram, then its opposite angles are congruent. Therefore, ∠ 2 is congruent with the angle that measures 79^(∘).
∠ 2 ≅ 79^(∘)
The definition of congruent angles tells us that their measures are equal, so m∠ 2=79^(∘).
Measure of ∠ 1
We see that ∠ 1 and ∠ 2 are consecutive angles. We recall that consecutive angles in a parallelogram are supplementary. Therefore, the sum of their angle measures is 180 ^(∘).
m∠ 1 + m∠ 2 = 180
Let's substitute 79 for m ∠ 2 and solve the resulting equation.
To find m∠ 3 we can use that ∠ 3 and ∠ 1 are opposite angles in a parallelogram, which makes them congruent.
∠ 3 ≅ ∠ 1
Therefore, their angle measures are equal, so m∠ 3=101^(∘). Let's gather the results we found!
