Question

The sum of the measures of the interior angles of a triangle is 180 °. The measure of the 1st angle is 15 ° less than the 2nd. The measure of the 3rd angle is 45 ° more than half of the second. Find the measure of e/ interior angle of the triangle.

Answer 1

1st angle (x): x - 15

2nd angle (y): x

3rd angle (z):
`(1)/(2)`x + 45

The sum of the interior angles of a triangle equals 180°

1st angle + 2nd angle + 3rd angle = 180

x - 15 + x +
`(1)/(2)`x + 45 = 180

2x + 30 +
`(1)/(2)`x = 180 (added like terms on left side)

2x +
`(1)/(2)`x = 150 (subtracted 30 from both sides)

4x + x = 300 (multiplied all terms by 2 to eliminate the denominator)

5x = 300 (added like terms on left side)

x = 60 (divided by 5 on both sides)

1st angle (x): x - 15 → (60) - 15 = 45

3rd angle (z):
`(1)/(2)`x + 45 →
`(1)/(2)`(60) + 45 → 30 + 45 = 75

Answer: 45°, 60°, 75°