Question

find the value of x. then find the measure of each labeled angle.
14.
15.
16.

1. x =
2. x =
3. x =

angle measures:
angle measures:
angle measures:

Explanation:

Problem 14

Step1: Use the property of consecutive interior angles

Consecutive interior angles are supplementary. So \(x+(x + 40)=180\).

Step2: Solve the equation

$$
LATEXBLOCK0
$$

Step3: Find the angle measures

One angle is \(x = 70^{\circ}\), and the other is \(x + 40=70+40 = 110^{\circ}\)

Step1: Use the property of corresponding angles and exterior - angle

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So \(3x-10=x + 40+x\)

Step2: Solve the equation

$$
LATEXBLOCK0
$$

Step3: Find the angle measures

One angle is \(x + 40=50+40 = 90^{\circ}\), and the other is \(3x-10=3\times50-10=140^{\circ}\)

Step1: Use the property of consecutive interior angles in a parallelogram - like figure (sum of adjacent angles is \(180^{\circ}\))

\(5x+4x=180\)

Step2: Solve the equation

$$
LATEXBLOCK0
$$

Step3: Find the angle measures

One angle is \(5x=5\times20 = 100^{\circ}\), and the other is \(4x=4\times20=80^{\circ}\)

Answer:

\(x = 70\), Angle measures: \(70^{\circ}\), \(110^{\circ}\)

Problem 15