You have to use the right angle if you want to find the measure of y^(∘).
x^(∘)=60^(∘)
y^(∘)=120^(∘)
Practice makes perfect
From the diagram, we can see that there is an equilateral triangle. According to the Corollary to the Base Angles Theorem, if a triangle is equilateral, then it is equiangular.
We know from the Triangle Sum Theorem, that the measures of a triangle's angles add up to 180^(∘). Therefore, each of the three angles in the equilateral triangle has a measure of 60^(∘).
180^(∘)/3=60^(∘)
This means we can conclude that x^(∘)=60^(∘). Let's add this information to our diagram.
Now we will turn to the second triangle. We can identify it as isosceles as two of its sides are the same length. According to the Base Angles Theorem, if two sides of a triangle are congruent, then the angles opposite them are congruent. We will add this information and labels to our diagram.
Notice that ∠ 1 is complementary to one of the equilateral triangle's base angles, which is 60^(∘). Using the Angle Addition Postulate we can write the following equation.
60^(∘)+m∠ 1=90^(∘)
Let's solve this equation.
