Question

If m∠BAC=(7x+1)° and m∠BCA=(5x+9)°, what is the measure of the vertex angle? Show your work to support your answer.

Answer 1

128degrees

Explanation:

Note that the given triangle ABC is an isosceles triangle with base angles equal, hence;

m∠BAC = m∠BCA

7x+1 = 5x+9

7x - 5x = 9-1

2x = 8

x = 8/2

x = 4

m∠BAC = 5x+6

m∠BAC = 5(4)+6

m∠BAC = 26 degrees

The vertex angle = 180 - (26+26)

The vertex angle = 180 - 52

The vertex angle = 128degrees