Question

question 10
it is given that ∠c and ∠d are supplementary. also, m∠c = 45° + y and m∠d = 35° + 3y. what is the angle measurement of ∠c?
hint: supplementary means two angles add to 180 degrees. to find the angle measurement of c, we must solve for y. (45 + y + 35 + 3y = 180) dont forget to plug the value of y back into 45 + y.
a 25°
b 70°
c 110°

Explanation:

Step1: Combine like terms

$$45 + y+35 + 3y=180$$
$$(45 + 35)+(y + 3y)=180$$
$$80+4y=180$$

Step2: Solve for \(y\)

Subtract \(80\) from both sides:
$$4y=180 - 80$$
$$4y=100$$
Divide both sides by \(4\):
$$y = 25$$

Step3: Find \(m\angle C\)

Substitute \(y = 25\) into \(m\angle C=45 + y\)
$$m\angle C=45+25$$
$$m\angle C = 70^{\circ}$$

Answer:

B. \(70^{\circ}\)