Question

Find the values of the variables and the measures of the angles

Answer 1

Explanation:

3x + 4x - 1 = 90⁰

7x = 91

x = 13

Angles are = 39 , 51⁰

Answer 2

The angles of the triangle are 39°, 51°, and 90°.

Explanation:

Step 1:

The sum of all the angles in any triangle is equal to 180°.

We have two of the three angles in terms of x while the third angle is not given directly. Since it is a right-angled triangle, one of the angles equals 90°.

So the angles of the triangle are
`3x,`
`4x-1,` and
`90.`

Step 2:

Now, we substitute all the angles to a sum of 180 to determine the value of x.

`3x + 4x - 1 + 90 = 180.`

`7x = 91, x = (91)/(7) = 13.`

So x = 13°. The angles are

`3x = 3 (13) = 39, 4x-1 = 4(13) - 1 = 51.`

The angles of the triangle are 39°, 51°, and 90°.