Question

18c) Find the value of x in each case.

Answer 1

Answer:

x = 22.5°

Step-by-step explanation:

m∠DEA = 2x

DE || AB

m∠EAB = 2x  - by Alternate Interior Angles

Exterior angle = 6x, which equals 2x + 4x

m∠BEA = 4x

Exterior Angle 4x = 2x + 2x

m∠B = 2x

2x + 4x + 2x = 180°

8x = 180°

x = 22.5°

Exterior Angles of a Triangle:

An exterior angle of a triangle is equal to the two REMOTE angles inside the triangle.

In this example, we know that 6x has remote angles of ∠EAB and ∠BEA

We found out that m∠EAB = 2x, so m∠BEA must equal 6x - 2x or 4x

Sum of angles in a Triangle:

The sum of all angles in a triangle is equal to 180°.

In this example, we found all the angles, 2x, 4x, 2x. We added all of those values to equal 8x

Since the sum of all angles = 180°:

8x = 180°

x = 180°/8

x = 22.5°

-Chetan K