Answer:
The angles measures are [37.5°], [75°], and [67.5°]
Step-by-step explanation:
Let us revise a fact about any triangle
- In any triangle, the sum of the measures of the interior angles of a triangle is 180°
We will use this fact to solve the question
∵ The measures of the angles of the given triangle are x°, 2x°, (x + 30)°
→ By using the fact above, equate their sum by 180°
∴ x + 2x + x + 30 = 180
→ Add the like terms in the left side
∴ (x + 2x + x) + 30 = 180
∴ 4x + 30 = 180
→ Subtract 30 from both sides
∴ 4x + 30 - 30 = 180 - 30
∴ 4x = 150
→ Divide both sides by 4 to find the value of x
∴ [tex]\frac{4x}{4}=\frac{150}{4}[/tex]
∴ x = 37.5
→ Substitute x by 37.5 in each angle
∴ x° = 37.5°
∴ 2x° = 2(37.5)° = 75°
∴ (x + 30)° = (37.5 + 30)° = 67.5°
The angles measures are [37.5°], [75°], and [67.5°]
To justify the answer substitute x by 37.5 in the equation
∵ 4x + 30 = 180
∵ x = 37.5
→ Left side = 4(37.5) + 30 = 150 + 30 = 180
→ Right side = 180
∵ Left side = Right side
∴ x = 37.5 is a correct answer.
