Question

∠a is supplementary to ∠b. m∠a=(7x + 4)° and m∠b=(3x + 6)°. find the value of x.
a. x = 17
b. x = 27
c. x = 90
d. x = 45

Explanation:

Step1: Recall supplementary - angle property

Supplementary angles add up to 180°. So, \(m\angle A + m\angle B=180^{\circ}\).
$$(7x + 4)+(3x + 6)=180$$

Step2: Combine like - terms

Combine the \(x\) terms and the constant terms on the left - hand side.
$$(7x+3x)+(4 + 6)=180$$
$$10x+10 = 180$$

Step3: Isolate the variable term

Subtract 10 from both sides of the equation.
$$10x+10−10=180−10$$
$$10x=170$$

Step4: Solve for \(x\)

Divide both sides by 10.
$$\frac{10x}{10}=\frac{170}{10}$$
$$x = 17$$

Answer:

A. \(x = 17\)