Question

in the figure, ( mangle 1=(2x)^circ ) and ( mangle 2=(x + 66)^circ ).
(a) write an equation to find ( x ). make sure you use an \=\ sign in your answer.
equation:
(b) find the degree measure of each angle.
( mangle 1=square^circ )
( mangle 2=square^circ )

Explanation:

Step1: Recognize supplementary angles

Angles 1 and 2 form a straight line, so they are supplementary (sum to $180^\circ$).
$2x + (x + 66) = 180$

Step2: Simplify and solve for x

Combine like terms and isolate x.
$3x + 66 = 180$
$3x = 180 - 66$
$3x = 114$
$x = \frac{114}{3} = 38$

Step3: Calculate $m\angle1$

Substitute x into the expression for $\angle1$.
$m\angle1 = 2x = 2\times38 = 76$

Step4: Calculate $m\angle2$

Substitute x into the expression for $\angle2$.
$m\angle2 = x + 66 = 38 + 66 = 104$

Answer:

(a) Equation: $2x + (x + 66) = 180$
(b) $m\angle1 = 76^\circ$
$m\angle2 = 104^\circ$