Question

One angle in a triangle has a measure that is three times as large as the smallest angle. The measure of the

third angle is 10 degrees more than that of the smallest angle. Find the measure of the LARGEST angle.

Answer 1

`102\textdegree`

Explanation:

If we let the measure of the smallest angle be
`x`, then we know that the measure of the angle that is three times as large as it is
`3*x=3x` and the measure of the angle that is
`10\textdegree` larger than it is
`x+10`.

Because the sum of the measures of the interior angles in a triangle is
`180\textdegree`, we can write the following equation to solve for
`x`:

`x+3x+x+10=180`

Solving for
`x`, we get:

`x+3x+x+10=180`

`5x+10=180` (Combine like terms)

`5x=170` (Subtract
`10` from both sides of the equation to isolate
`x`, Simplify)

`x=34\textdegree`

Therefore, the measures of the other angles are
`3x = 3 * 34=102\textdegree` and
`34+10=44\textdegree`. Since
`102>44>34`, the measure of the largest angle will be
`\bf102\textdegree`. Hope this helps!