Question

station 3
find the value of x for each triangle
a.
b.

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). For part a, we have the equation \(x + 40^{\circ}+80^{\circ}=180^{\circ}\).

Step2: Solve for \(x\) in part a

$$
LATEXBLOCK0
$$

Step3: Use the triangle angle - sum theorem for part b

Since one angle is \(90^{\circ}\) (right - triangle), we have the equation \((2x + 1)+(5x + 5)+90=180\).

Step4: Simplify the equation for part b

$$
LATEXBLOCK1
$$

Step5: Solve for \(x\) in part b

$$
LATEXBLOCK2
$$

Answer:

a. \(x = 60^{\circ}\)
b. \(x = 12\)