Question

Need help solving this problem

Answer 1

x = 9

y = 105

Explanation:

Corresponding angles are pairs of angles that occupy the same relative positions at the intersection of two parallel lines when a transversal line cuts through them, and they are equal in measure.

Assuming that the horizontal lines in the given diagram are parallel, the corresponding angles are labelled (8x + 3)° and (5x + 30)°. Therefore, to find the value of x, set the corresponding angles equal to each other and solve for x:

(8x + 3)° = (5x + 30)°

8x + 3 = 5x + 30

8x + 3 - 5x = 5x + 30 - 5x

3x + 3 = 30

3x + 3 - 3 = 30 - 3

3x = 27

3x / 3 = 27 / 3

x = 9

Therefore, the value of x is 9.

Given that angles on a straight line add up to 180°, we can determine the value of y by setting the sum of angle y° and angle (8x + 3)° equal to 180°, substituting the known value of x, and subsequently solving for y:

y° + (8x + 3)° = 180°

y + 8x + 3 = 180

y + 8(9) + 3 = 180

y + 72 + 3 = 180

y + 75 = 180

y + 75 - 75 = 180 - 75

y = 105

Therefore, the value of y is 105.

Answer 2

x = 9

y = 105

Explanation:

Corresponding angles are two angles that are located in the same corresponding positions relative to a transversal that intersects two parallel lines.

Corresponding angles are always congruent, meaning they have the same measure.

Using this, we can say that

5x + 30 and 8x + 3 are corresponding angles.

So,

5x + 30 = 8x + 3

Subtract 5x on both sides.

5x + 30 - 5x = 8x + 3 - 5x

30 = 3x + 3

Subtract 3 on both sides.

30 - 3 = 3x + 3 - 3

27 = 3x

Divide both sides by 3.

`\sf (27)/(3)=(3x)/(3)`

x = 9

Again,

we know that.

A linear pair is a pair of adjacent angles that form a straight line. Linear pairs are always supplementary, meaning their measures add up to 180 degrees.

Using this , we can say that:

y and 8x + 3 are linear pair

So,

y + 8x + 3 = 180°

Substituting value of x.

y + 8 × 9 + 3 = 180°

y + 72 + 3 = 180

y + 75 = 180

Subtract 75 on both sides.

y + 75 - 75 = 180 - 75

y = 105

Therefore, value of x is 9 and value of y is 105.