Question

The vertex angle of an isosceles triangle is 42 more than 3 times the base angles. Find the vertex angle.

a The vertex angle is 124.8°.

b The vertex angle is 27.6°.

c The vertex angle is 40.8°.

d The vertex angle is 82.8°.​

Answer 1

a

Explanation:

The sum of the 3 angles in a triangle = 180°

let x be the base angles, then vertex angle is 3x + 42

Sum the 3 angles and equate to 180, that is

x + x + 3x + 42 = 180

5x + 42 = 180 ( subtract 42 from both sides )

5x = 138 ( divide both sides by 5 )

x = 27.6

Thus

vertex angle = 3x + 42 = 3(27.6) + 42 = 82.8 + 42 = 124.8° → a

Answer 2

Answer: 124.8°

Explanation:

1) Make an equation:
`(3x+42)+x+x=180`

2) Expand and simplify the equation:
`5x+42=180`

3) Solve the equation:

a)
`5x= 138`

b)
`x= 27.6`

4) Substitute it into the original expression: 3x+42:
`3(27.6)+42= angle`

5) Solve the equation:
`angle= 124.8`