Question

15
two supplementary angles are given. find the value of x and the given angle.
$m\angle w = 72^\circ$ and $m\angle y = (4x - 12)^\circ$
write the equation:
$x = $
$m\angle y = $ degrees

Explanation:

Step1: Define supplementary angles sum

Supplementary angles sum to $180^\circ$, so set up the equation:
$$72 + (4x - 12) = 180$$

Step2: Simplify the left side

Combine constant terms:
$$4x + 60 = 180$$

Step3: Isolate the variable term

Subtract 60 from both sides:
$$4x = 180 - 60$$
$$4x = 120$$

Step4: Solve for x

Divide both sides by 4:
$$x = \frac{120}{4}$$
$$x = 30$$

Step5: Calculate $m\angle Y$

Substitute $x=30$ into the angle expression:
$$m\angle Y = 4(30) - 12$$
$$m\angle Y = 120 - 12$$
$$m\angle Y = 108$$

Answer:

Write the equation: $72 + (4x - 12) = 180$
$x = 30$
$m\angle Y = 108$ degrees