Question

one angle of a triangle measures 130°. the other two angles are in a ratio of 2:3. what are the measures of those two angles? ° and °

Explanation:

Step1: Find the sum of the other two angles

The sum of angles in a triangle is 180°. One angle is 130°, so the sum of the other two angles is $180 - 130=50^{\circ}$.

Step2: Set up an equation based on the ratio

Let the two angles be 2x and 3x. Then $2x + 3x=50$. Combining like - terms gives $5x = 50$.

Step3: Solve for x

Dividing both sides of the equation $5x = 50$ by 5, we get $x=\frac{50}{5}=10$.

Step4: Find the measures of the two angles

The first angle is $2x = 2\times10 = 20^{\circ}$, and the second angle is $3x=3\times10 = 30^{\circ}$.

Answer:

20, 30