Question

NOT DRAWN TO SCALE.

In blank 1, give the value of x.

In blank 2, give the m∠AEB. Do not type degrees just the number.

In blank 3, give the value of y. Do not type degrees just the number.



Question 3 options:
Blank # 1
Blank # 2
Blank # 3

Answer 1

Explanation:

<AEB = < CED by vertical pairs

5x-9 = 3x+31

2x = 40

x = 20

5(20) - 9 = 100-9 = 91

<CED = <AEB by vert pairs (91)

<AEB + <AED = <BED (linear pairs)

91 + y = 180

y = 89

Answer 2

The value of x is 20. The value of <AEB is 91. The value of y is 89. Blank 1 _20__ , blank 2 __91_, blank3 _89__.

According to the given diagram, line AEC and BED are parallel to each other.

Solve for Blank 1:

Here, <AEB is equal to <DEC because both are vertically opposite angles.

So, we can write:

<AEB = <DEC

Substituting the values:

5x-9 = 3x+31

This implies:

2x = 40

=> x = 20

Solve for Blank 2 and Blank 3:

Here, <DEB is 180 degree because DEB is a straight line whose value is always 180.

Now, according to the figure, we can write:

<AED + <AEB = <DEB

Substituting the values:

y + (5x-9) = 180

Putting the value of X:

y + 100-9 =180

=> y = 180 - 91

=> y = 89

Now,

<AEB = 5x - 9

=> <AEB = 100 -9 = 91

Question:

In blank 1, give the value of x.

In blank 2, give ∠AEB. Do not type degrees just the number.

In blank 3, give the value of y. Do not type degrees just the number.

Blank 1 ___

Blank 2 ___

Blank 3 ___