Question

The measures of the angles in a triangle are 1.5x, 2.4x, and 3.3x. Write an equation to determine the measure of each angle in the triangle. Use the equation to determine the exact measure of each angle in the triangle.

Answer 1

`37.5^(\circ)\,,\,60^(\circ)\,,\,82.5^(\circ)`

Explanation:

Given: measures of the angles in a triangle are
`1.5x,2.4x,3.3x`

To find: equation to determine the measure of each angle in the triangle and exact measure of each angle in the triangle

Solution:

According to angle sum property, sum of angles of a triangle is
`180^(\circ)`

So, equation to determine the measure of each angle in the triangle is
`1.5x+2.4x+3.3x=180^(\circ)`

`1.5x+2.4x+3.3x=180^(\circ)\\7.2x=180^(\circ)\\x=(180^(\circ))/(7.2)=25^(\circ)`

So,

`1.5x=1.5(25^(\circ))=37.5^(\circ)\\2.4x=2.4(25^(\circ))=60^(\circ)\\3.3x=3.3(25^(\circ))=82.5^(\circ)`