Question

Please help me solve. Use the diagram below to answer the following questions

A. What is the value of X

B. Measure of angle AOB

C. Measure of AOE

Answer 1

I jus did a test on it and it’s c I jus got it right

Answer 2

The sum of all the angle on a straight line is equal to the 180 degrees.

• The value of $x$ is 26 degree.

• The measure of the $\angle AOB$ is 50 degrees.

• The measure of the $\angle AOE=$ is 130 degrees.

What is the angle of straight line?

Angle on one side of a straight line is always equals to the 180 degrees.

Given information-

In the given figure the $\angle AOB$ is $(3x-28)$.

The $\angle BOC$ is right angle triangle measure 90 degree.

The $\angle COD$ is $(366-x)$.

• A) The value of $x$.

As $AD$ is straight line. The sum of all the angle on a straight line is equal to the 180 degrees. thus,

$\angle AOB+\angle BOC+\angle COD=180$

Put the values,

$\begin{aligned}\\(3x-28)+90+(66-x)&=180\\3x-x-28+90+66&=180\\2x+128&=180\\2x&=180-128\\x&=\dfrac{52}{2}\\ x&=26\\\end$

Hence the value of $x$ is 26 degree.

• B) Measure of angle AOB

$\angle AOB=(3x-28)\\\angle AOB=3\times26-28\\\angle AOB=78-28\\\angle AOB=50$

Hence, the measure of the $\angle AOB$ is 50 degrees.

• C) B) Measure of angle AOE

As $BE$ is straight line. The sum of all the angle on a straight line is equal to the 180 degrees. thus,

$\angle AOB+\angle AOE=180$

Put the values,

$50+\angle AOE=180\\\angle AOE=180-50\\\angle AOE=130$

Hence, the measure of the $\angle AOE=$ is 130 degrees.

Thus,

• The value of $x$ is 26 degree.
• The measure of the $\angle AOB$ is 50 degrees.
• The measure of the $\angle AOE=$ is 130 degrees.

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