Question

Write an equation that relates the angles in a triangle.

9. The measure of angle A is 45 degrees. The measure of angle B is b
degrees. The measure of angle C is 3b degrees.
_________________________________________________________________________________________
10. The measures of angles X and Y are the same, x degrees. The
measure of angle Z is twice the measure of angle Y.
_________________________________________________________________________________________

Answer 1

9.
`4b^\circ` =
`135^\circ`

10. 4
`x^\circ`=
`180^\circ`

Explanation:

9.

Given that, the measure of
`\angle A` is
`45^\circ`. The measure of
`\angle B`is
`b^\circ`. The measure of
`\angle C` is
`3b^\circ` .

We know that the sum of all angles of triangle is
`180^\circ`.

Therefore

`45^\circ + b^\circ +3b^\circ =180^\circ`

⇔
`4b^\circ` =
`135^\circ`

10.

Given that , the measure of
`\angle X` and
`\angle Y`are same
`x^\circ`. The angle of
`\angle Z` is twice the measure of
`\angle Y`.

∴
`\angle X`+
`\angle Y`+
`\angle Z`=
`180^\circ`

⇔
`x^\circ`+
`x^\circ`+2
`x^\circ`=
`180^\circ`

⇔4
`x^\circ`=
`180^\circ`