Let's begin by finding the measure of ∠ a first. Then, we will find the measures of ∠ b and ∠ c.
Measure of ∠ a
Notice that ∠ a and the exterior angle with measure 110 form a linear pair. If two angles form a linear pair, then they are supplementary. By the definition of supplementary angles, we can conclude that the sum of a and 110 is 180.
a + 110 = 180
Now, we can subtract 110 from both sides of our equation and find the measure of ∠ a.
a = 180-110 ⇔ a = 70
Measure of ∠ b
We can tell that ∠ b and ∠ c are congruent. By the definition of congruent angles, we can conclude that their measures are equal, b= c. Next, by the Exterior Angle Theorem, the sum of their measures is equal to 110.
b + c = 110
By the Substitution Property of Equality, we can substitute c for b in our equation.
c+ c = 110 ⇔ 2c = 110
Now, we can divide both sides by 2 and find the measure of ∠ c.
c = 1102 ⇔ c = 55
Recall that we know that c = b. Therefore, the measure of ∠ b is also 55.
Conclusion
We can conclude that the measure of ∠ a is 70 and the measure of ∠ b and ∠ c is 55.
a=70, b = 55, c=55
