Question

Examine the diagram. Triangle M P L. Angle P is 90 degrees and angle L is (4 x + 6) degrees. The exterior angle to angle M is 136 degrees. What is the value of x?

Answer 1

x =
`10^(0)`

Explanation:

From Δ MPL given that; <P =
`90^(0)`, exterior angle to M =
`136^(0)` and <L =
`(4x+6)^(0)`.

In the triangle, the exterior angle is equal to the sum of the two adjacent interior angles. So that;

`136^(0)` =
`90^(0)` +
`(4x+6)^(0)`

=
`90^(0)` + 4
`x^(0)` +
`6^(0)`

`136^(0)` =
`96^(0)` +
`x^(0)`

⇒ 4
`x^(0)` =
`136^(0)` -
`96^(0)`

4
`x^(0)` =
`40^(0)`

Divided both sides by 4 to have;

`x^(0)` =
`10^(0)`

The value of x is
`10^(0)`.