Question

1. Given a right triangle the first angle is ten degrees more than three times the degree measure of the second angle and the third angle is the right angle. What is the angle measurement of the first angle? Doint)​

Answer 1

The first angle is
`70^(o)`.

Explanation:

Let the measure of the second angle be represented by
`x^(o)`.

Thus, the first angle =
`(3x+10)^(o)`

Third angle =
`90^(o)`

Sum of angles in a triangle =
`180^(o)`

So that;

`x^(o)` +
`(3x+10)^(o)` + 90 =
`180^(o)`

`x^(o)` +
`3x^(o)` +
`100^(o)` =
`180^(o)`

`4x^(o)` =
`180^(o)` -
`100^(o)`

`4x^(o)` =
`80^(o)`

divide both sides by 4 to have;

`x^(o)` =
`20^(o)`

The first angle =
`(3x+10)^(o)`

= ( 3 x 20 + 10)

= 60 + 10

=
`70^(o)`

Therefore, the first angle is
`70^(o)`.