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!
