Question

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Answer 1

We know that:

Since line m is parallel to line n, (6x - 5) and (6x + 5) are a linear pair.

Linear pair means that the sum of two angles equaling 180°.

This means that:

`(6x - 5) + (6x + 5) = 180`

Step-by step calculations:

Opening the parenthesis:

`(6x - 5) + (6x + 5) = 180 \\\\6x - 5 + 6x + 5 = 180`

Combining like terms:

`6x - 5 + 6x + 5 = 180 \\\\ (6x + 6x) + (-5 + 5) = 180`

Simplify the LHS:

`(6x + 6x) + (-5 + 5) = 180\\\\(12x) = 180`

Divide 12 both sides and simplify:

`(12x)/(12) = (180)/(12) \\\\ x = 15`

Thus, the value of x is 15.

Answer 2

x = 15°

Explanation:

Linear pair = 180°

⇒ (6x - 5) + (6x + 5) = 180°

⇒ 12x = 180°

⇒ x = 15°