Question

determine the value of x. a. x = 90 b. x = 10 c. x = 76 d. x = 80

Explanation:

Step1: Recall angle - sum property

The sum of the three angles shown is 180° since they form a straight - line. One angle is 90° (right - angle), another is 12°, and the third is \((x - 2)^{\circ}\). So, \(90+12+(x - 2)=180\).

Step2: Simplify the left - hand side

First, simplify \(90 + 12+(x - 2)\):
\[

$$\begin{align*} 90+12+(x - 2)&=(90 + 12-2)+x\\ &=(102-2)+x\\ &=100 + x \end{align*}$$

\]
So the equation becomes \(100 + x=180\).

Step3: Solve for x

Subtract 100 from both sides of the equation \(100 + x=180\):
\(x=180 - 100\)
\(x = 80\)

Answer:

D. \(x = 80\)