Question

Solve for y and the measure of the vertex angle.

Answer 1

The required values are:

i. x = 11 in.

ii. y = 6 in.

iii. Vertex angle P =
`20^(o)`

An isosceles triangle is a type of triangle which has two sides to be equal, and equal base angles. So that from the given question, we have;

i. (8x - 8) = (25 + 5x)

8x - 5x = 25 + 8

3x = 33

x = 11

So that:

(8x - 8) = 8(11) - 8

=
`80^(o)`

(25 + 5x) = 25 + 5(11)

= 25 + 55

=
`80^(o)`

ii. Since the two sides are congruent, then;

(x + y) = (3y - 1)

11 + y = 3y -1

11 + 1 = 3y - y

12 = 2y

y = 6

iii. <P + <H + <G = 180

<P + 80 + 80 = 180

<P = 180 - 160

= 20

<P =
`20^(o)`