Question

Line a || Line b.

Use the diagram to write an equation and solve for x.

Answer 1

Given that line a is parallel to line b . And we need to solve out the value for x .

The two unknown angles are 2x -15 and 3x +5 . (See attachment)

So from the figure ,

• angle f = angle 2x -15 ( vertically opposite angles) ..... (i)

Again

• angle f = angle c ( alternate interior angles)..... (ii)

and,

• sum of angle c and (3x+5) will be 180° (linear pair ) ..... (iii)

Hence from i , ii and iii , we have;

`\longrightarrow 2x -15+3x+5=180^o\\`

Add 10 to both sides ,

`\longrightarrow 5x -10=180^o\\`

divide both the sides by 5 ,

`\longrightarrow 5x = 190^o\\`

`\longrightarrow \underline{\underline{x =38^o}}`

And we are done!

Answer 2

(2x - 15)° + (3x + 5)° = 180°

x = 38

Explanation:

Same-side Exterior Angles Theorem

When two parallel lines are intersected by a transversal, the angles that are exterior to the parallel lines and on the same side of the transversal line are supplementary (sum to 180°).

From the given diagram:

• Line a is parallel line b.
• Line t is the transversal.

Therefore, according to the same-side exterior angles theorem:

⇒ (2x - 15)° + (3x + 5)° = 180°

⇒ 2x - 15 + 3x + 5 = 180

⇒ 2x + 3x - 15 + 5 = 180

⇒ 5x - 10 = 180

⇒ 5x - 10 + 10 = 180 + 10

⇒ 5x = 190

⇒ 5x ÷ 5 = 190 ÷ 5

⇒ x = 38

Therefore, x is 38.