Answer:
x = 36°, 2x° = 72°, 3x° = 108°, and 4x° = 144°
Step-by-step explanation:
Given the quadrilateral in which the sum of its four angles is 360°.
We can establish the following formula to find the value of x, and determine the measures of each angle:
x° + 2x° + 3x° + 4x° = 360°
Combine like terms:
10x° = 360°
Divide both sides by 10 to solve for x:
[tex]\mathsf{\frac{10x^{\circ}}{10}\:=\: \frac{360^{\circ}}{10}}[/tex]
x = 36°
Substitute the value of x into each unknown angle measures:
x = 36°
2x° = 2(36)° = 72°
3x° = 3(36)° = 108°
4x° = 4(36)° = 144°
Verify whether the sum of the previously unknown angle measures equal 360°:
x° + 2x° + 3x° + 4x° = 360°
36° + 72° + 108° + 144° = 360°
360° = 360° (True statement).
Therefore, the following are the angle measures of the given quadrilateral: x = 36°, 2x° = 72°, 3x° = 108°, and 4x° = 144°
