Answer:
m∠1 = 22°
Step-by-step explanation:
Given the ∠WXZ = m∠66°, which includes the following adjacent angles:
∠WXY = m∠1
∠YXZ = m∠2
The prompt also states that m∠2 is twice the measure of ∠1.
Hence, let m∠1 = x, and m∠2 = 2x.
In order to find m∠1, we can establish the following formula:
m∠1 + m∠2 = m∠WXZ
Substitute the given values into the formula:
x + 2x = 66°
Combine like terms on the left-hand side:
3x = 66°
Divide both sides by 3 to solve for x:
[tex]\displaystyle\mathsf{\frac{3x^{\circ}}{3^{\circ}}\:=\:\frac{66^{\circ}}{3^{\circ}} }[/tex]
x = 22°
Therefore, the value of m∠1 = 22°, and m∠2 = 2x = 2(22)° = 44°.
Double-check:
In order to verify whether we have the correct values for m∠1 and m∠2, substitute their values into the equation:
m∠1 + m∠2 = m∠WXZ
x + 2x = 66°
22° + 44° = 66°
66° = 66° (True statement).
