Question

The measure of one angle of a triangle is 105°. The measure of the

other two angles are in a ratio of 2:3. What are the unknown angle
measures? Show your work for credit.
2:3
105T

Answer 1

The unknown angle measures are 30° and 45°.

Step-by-step explanation:

Let the measures of the other two angles be 2x and 3x.

Since the sum of the measures of the angles in a triangle is 180°, we can write the equation:

105° + 2x + 3x = 180°

Combining like terms, we get:

5x + 105° = 180°

Subtracting 105° from both sides, we get:

5x = 75°

Dividing both sides by 5, we get:

x = 15°

Therefore, the measures of the other two angles are:

2x = 2(15°) = 30°

3x = 3(15°) = 45°

So, the unknown angle measures are 30° and 45°.

Learn more about Triangle angles