Question

two parallel lines AB and CD are cut by a transversal EF. if the if the interior angles of the same side of EF be (4x + 27°) and (7x - 12°) find the measure of each of the angles​

Answer 1

Hello !

Refer to the attachment. for the diagram.

Property to be used:-

The sum of interior angles is 180⁰

Solution:-

$\implies$ 4x+27⁰+(7x-12)⁰ = 180⁰

$\implies$ 4x+27⁰+7x-12⁰=180⁰

$\implies$ 11x+15 = 180⁰

$\implies$ 11x = 165⁰

$\implies$ x = $\cancel\dfrac{165}{11}$

$\implies$ x = 15⁰

Now let's find the value of both the angles.

$\implies$ 4x+27 = 4(15)+27 = 87⁰

$\implies$ 7x-12 = 7(15)-12 = 93⁰

Verification:-

to check whether our answer is right or not, we can use this interior angle property as :-

87⁰+93⁰ = 180⁰

Hope that helps !