Question

4. Part A. Find the value of x.

Answer 1

Hey there!!

The measure of the unlabeled angle is ( x + y - 5 ) due to the vertically opposite angles.

We also know 2x = y due to vertically opposite angles

If we add up all the angles, we get 360 degrees.

Hence,  

y + 2x + x + y - 5 + x + y - 5 = 360

4x + 3y - 10 = 360

Add 10 on both sides

4x + 3y = 370

We know 2x = y

Hence,

4x + 3y = 370 can be broken down as ,

4x + y + y + y = 370

4x + 2x + 2x + 2x = 370

10x = 370

x = 370 / 10

x = 37

The unknown angle = x + y - 5

x + 2x - 5

3x - 5

3 ( 37 ) - 5

111 - 5

106

Hence, the unknown angle is 106°

Hope my answer helps!!

Answer 2

Part A: B)35
As the angle y° equals to angle 2x°, y=2x.
And the sum of the angle (x+y+5°)and the angle 2x° is 180°.Therefore,
x+y+5°+2x =180°
x+2x+5°+2x=180°
5x+5° =180°
5x =175°
x =35°


Part B: C)110°
As I said, y =2x
And the unlabled angle eaquals to the angle(x+y+5°).
Therefore,
the unabled angle= x+y+5°
=x+2x+5°
=3x+5°
=3(35°)+5°
=110°