Final answer:
To find the measures of the two unknown angles in a triangle with angles in a ratio of 13:18 and one known angle of 25°, solve the equation 25 + 13x + 18x = 180. After finding x equals 5, determine the angle measures to be 65° and 90°.
Step-by-step explanation:
The sum of angles in a triangle is always 180 degrees. Given that one angle measures 25° and the other two have a ratio of 13:18, we can denote the two unknown angles as 13x and 18x respectively. The sum of the angles would thus be 25 + 13x + 18x = 180. This simplifies to 31x = 155, since 25° is subtracted from both sides of the equation.
Thus, x = 155 ÷ 31, which equals 5. Having found the value of x, we can now calculate the measures of the two remaining angles:
- The angle with ratio 13: 25° = 13×5 = 65°
- The angle with ratio 18: 25° = 18×5 = 90°
Therefore, the measures of the two angles are 65° and 90°.