Answer:
x = 3°
Step-by-step explanation:
Given the equilateral triangle with the following angles:
m∠1 = (21x - 3)°
m∠2 = (17x + 9)°
m∠3 = (15x + 15)°
In order to solve for the value of x, we must apply the Triangle Sum Theorem, which states that the sum of the measures of all interior angles of a triangle is 180°.
Thus, we can set up the following equation to solve for x:
m∠1 + m∠2 + m∠3 = 180°
(21x - 3)° + (17x + 9)° + (15x + 15)° = 180°
21x° - 3° + 17x° + 9° + 15x° + 15° = 180°
Combine like terms and constants:
21x° - 3° + 17x° + 9° + 15x° + 15° = 180°
53x° + 21° = 180°
Subtract 21° from both sides:
53x° + 21° - 21° = 180° - 21°
53x° = 159°
Divide both sides by 53 to solve for x:
[tex]\displaystyle\mathsf{\frac{53x^\circ}{53^\circ}\:=\:\frac{159^\circ}{53^\circ}}[/tex]
x = 3°
Therefore, the value of x = 3°.
Double-check:
In order to verify whether we have the correct value of x, we must substitute its value into the given angles:
m∠1 = (21x - 3)° = 21(3)° - 3° = 60°
m∠2 = (17x + 9)° = 17(3)° + 9° = 60°
m∠3 = (15x + 15)° = 15(3)° + 15° = 60°
m∠1 + m∠2 + m∠3 = 180°
60° + 60° + 60° = 180°
180° = 180° (True statement).
