Question

Use the fact that the sum of the 3 angles in a triangle is 180° to answer this question.One angle in a triangle has a measure that is three times as large as the smallest angle. Themeasure of the third angle is 20° more than that of the smallest angle. Find the measure of the eachof the angles.nsOThe SMALLEST angle has a measure of

Answer 1

Let us call the angles x, y , and z. We know that these three angles must add up to 180; therefore,

`x+y+z=180`

If x is the smallest angle, we know that one of the angles (call it y) is 3 times this angle; therefore,

`y=3x`

And the other angle z is 20 more than the smallest angle x; therefore, we have

`z=20+x`

Putting the last two equations into the very first equation gives us

`x+3x+20+x=180`
`5x+20=180`
`\textcolor{#FF7968}{\therefore x=32}`

which is the measure of the smallest angle.

The other two angles are

`y=3x=3(32)`
`\textcolor{#FF7968}{y=96}`

and

`z=20+x=20+32`
`\textcolor{#FF7968}{z=52.}`

Hence, the measure of the smallest angle is 32,

The measure of the middle angle is 52

And the measure of the largest angle is 96.