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 30 degrees more than that of the smallest angle. find the measure of the largest angle. answer: the largest angle has a measure of enter an integer or decimal number more... degrees.

Explanation:

Step1: Let the smallest angle be $x$ degrees.

The largest angle has a measure that is three times as large as the smallest angle, so the largest - angle is $3x$ degrees.
The third angle is $30$ degrees more than the smallest angle, so it is $(x + 30)$ degrees.

Step2: Use the angle - sum property of a triangle.

The sum of the interior angles of a triangle is $180$ degrees. So, $x+3x+(x + 30)=180$.

Step3: Simplify the left - hand side of the equation.

Combine like terms: $x+3x+x+30 = 5x+30$. So, $5x+30 = 180$.

Step4: Solve for $x$.

Subtract $30$ from both sides of the equation: $5x=180 - 30=150$.
Then divide both sides by $5$: $x=\frac{150}{5}=30$.

Step5: Find the measure of the largest angle.

The largest angle is $3x$. Substitute $x = 30$ into $3x$, we get $3\times30 = 90$ degrees.

Answer:

$90$