Question

A triangle has an angle that measures 105.6°. The other two angles are in a ratio of 14:17. What are the measures of those two angles?

Answer 1

`color(blue)(33.6^@)`

`color(blue)(40.8^@)`

Explanation:

All the angles in a triangle add to `180^@`, so the sum of the unknown angles is:

`180^@-105.6^@=74.4^@`

These are in a ratio of `14:17`

Add these:

`14+17=31`

Divide `74.4` by this:

`74.4/31`

Distribute this in the given ratio:

`14xx74.4/31=33.6`

`17xx74.4/31=40.8`

So the angles are:

`color(blue)(33.6^@)`

`color(blue)(40.8^@)`

Answer 2

The 2 angles are 33.6° and 40.8°.

Explanation:

We know, Sum of angles of a triangle = 180°
Also, if the angles are in the ratio 14:17, we know that the sum of the angles is `14x+17x`.
So, `180° =14x+17x+105.6°`
We can now simplify it, `180-105.6=31x`
`74.4/31=x`
`x=2.4`
Thus, `14x=2.4*14=33.6°`
And, `17x=2.4*17=40.8°`