Two parallel lines $l$ and $m$ cut by a transversal $t$. If the interior angles of the same side of $t$ be $(2 x-8)°$ and $(3 x-7)°$, find the measure of each of these angles.

Given :

The lines l and m are parallel and t is the transversal.

The interior angles on the same side of the transversal are $(2 x-8)°$ and $(3 x-7)°$.

To do :

We have to find each of the angles.

Solution :

We know that,

The sum of the interior angles on the same side of the transversal is 180°.

$(2 x-8)° + (3 x-7)° = 180°$

$2x + 3x -15° = 180°$

$5x = 180° + 15°$

$5x = 195°$

$x = \frac{195}{5} = 39°$

$2x -8 = 2(39) - 8 = 78 - 8 = 70°$

$3x-7 = 3(39)-7 = 117-7=110°$

Therefore, the measure of the angles are 70° and 110°.

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Updated on: 10-Oct-2022

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