Question

quiz 4-1 : classifying and solving for sides/angles in triangles gina wilson (all things algebra) URGENT

Answer 1

14.

`x = 11`
`m<B = 108`
`m<C= 36`
`m<D = 36`

15.

`x = 4`
`WX = 25`
`XY = 17`
`WY = 25`

Explanation:

Solving (14):

`BC = BD`

`m<B = 13x - 35`

`m<C = 5x - 19`

`m<D = 2x + 14`

First, we solve for x.

Since sides
`BC = BD`, then

`m<C = m<D`

This is so because the theorem of ASA (Angle-Side-Angle)

So, we have:

`5x - 19 = 2x + 14`

Collect Like Terms

`5x - 2x = 19 + 14`

`3x = 33`

Divide both sides by 3

`x = 11`

Solving for m<B, m<C and m<D.

We simply substitute 11 for x in their respective expressions.

`m<B = 13x - 35`

`m<B = 13*11 - 35`

`m<B = 143 - 35`

`m<B = 108`

`m<C = 5x - 19`

`m<C= 5*11 - 19`

`m<C= 55 - 19`

`m<C= 36`

`m<D = 2x + 14`

`m<D = 2*11 + 14`

`m<D = 22 + 14`

`m<D = 36`

Solving (15):

`<X = <Y`

`WX = 9x - 11`

`XY = 4x + 1`

`WY = 7x - 3`

First, we solve for x.

Since
`<X = <Y`, then

`WX = WY`

This is so because the theorem of SAS (Side-Angle-Side)

So, we have:

`9x - 11 = 7x - 3`

Collect Like Terms

`9x - 7x = 11-3`

`2x = 8`

Divide both sides by 2

`x = 4`

Solving for WX, WY and XY

We simply substitute 4 for x in their respective expressions.

`WX = 9x - 11`

`WX = 9 * 4 - 11`

`WX = 36 - 11`

`WX = 25`

`XY = 4x + 1`

`XY = 4 * 4 + 1`

`XY = 16 + 1`

`XY = 17`

`WY = 7x - 3`

`WY = 7 * 4 - 3`

`WY = 28 - 3`

`WY = 25`