Answer:
The value of x is 50
The measures of the 3 angles are 50°, 100°, 30°
Step-by-step explanation:
Let us solve the question
∵ The sum of the measures of the angles of a triangle is 180°
∵ The measures of the 3 angles of the given Δ are x°, 2x°, (x - 20)°
→ Add them and equate the sum by 180
∴ x° + 2x° + (x - 20)° = 180°
→ Add the like terms
∵ (x + 2x + x) + (-20) = 180
∴ 4x - 20 = 180
→ Add 20 to both sides
∵ 4x - 20 + 20 = 180 + 20
∴ 4x = 200
→ Divide both sides by 4 to find x
∴ x = 50
∴ The value of x is 50
To find the measures of the 3 angles substitute x by 50 in their expressions
∵ The measure of one angle is x
∴ The measure of the 1st angle is 50°
∵ The measure of the 2nd angle is 2x
∴ The measure of the 2nd angle = 2(50)
∴ The measure of the 2nd angle is 100°
∵ The measure of the 3rd angle is (x - 20)
∴ The measure of the 3rd angle = (50 - 20)
∴ The measure of the 3rd angle is 30°
∴ The measures of the 3 angles are 50°, 100°, 30°
radians.