Question

Please help Find: ∠x ∠a ∠b

Answer 1

x = 22

<a = 88°

<b = 92°

Explanation:

To solve for x, <a, and <b, we'd need to recall some of the properties of parallel lines, then apply them in solving this problem.

To find the value of x, recall that consecutive interior angles are supplementary. (5x - 18), and (3x + 22) are consecutive interior angles. Therefore:

`(5x - 18) + (3x + 22) = 180`

Solve for x

`5x - 18 + 3x + 22 = 180`

`5x + 3x - 18 + 22 = 180`

`8x + 4 = 180`

Subtract 4 from both sides:

`8x + 4 - 4 = 180 - 4`

`8x = 176`

Divide both sides by 8

`(8x)/(8) = (176)/(8)`

`x = 22`

=>Find <a:

According to the properties of parallel lines, alternate interior angles are equal. Therefore:

<a = 3x + 22

Plug in the value of x

<a = 3(22) + 22 = 66 + 22

<a = 88°

=>Find <b:

According to the properties of parallel lines, corresponding angles are said to be equal. Therefore,

<b = 5x - 18

Plug in the value of x to find <b

<b = 5(22) - 18

<b = 110 - 18 = 92°