Question

Using the figure to the right, if RSTU is a rhombus, find measure RST.

Answer 1

Given:

In rhombus RSTU,
`m\angle RUV=(10x-23)^\circ` and
`m\angle TUV=(3x+19)^\circ`.

To find:

The
`m\angle RST`.

Solution:

We know that, diagonals of a rhombus are angle bisector. So,

`m\angle RUV=m\angle TUV`

`(10x-23)^\circ=(3x+19)^\circ`

`10x-23=3x+19`

Isolating variable terms, we get

`10x-3x=23+19`

`7x=42`

Divide both sides by 7.

`x=(42)/(7)`

`x=6`

Now,

`m\angle RUV=(10x-23)^\circ`

`m\angle RUV=(10(6)-23)^\circ`

`m\angle RUV=(60-23)^\circ`

`m\angle RUV=37^\circ`

And,

`m\angle TUV=(3x+19)^\circ`.

`m\angle TUV=(3(6)+19)^\circ`

`m\angle TUV=(18+19)^\circ`

`m\angle TUV=37^\circ`

Now,

`m\angle RUT=m\angle RUV+m\angle TUV`

`m\angle RUT=37^\circ+37^\circ`

`m\angle RUT=74^\circ`

We know that opposite angles of a rhombus are equal.

`m\angle RST=m\angle RUT`

`m\angle RST=74^\circ`

Therefore, the measure of angle RST is
`74^\circ`.