Two parallel lines $l$ and $m$ are cut by a transversal $t$ . If the interior angles on the same side of the transversal $t$ be $2 x - 9$ and $3 x - 7$ . Find the measure of each angle.

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Solution

Given $(2 x - 9)$ and $(3 x - 7)$ are interior angles of the same side of the transversal .

we know that, sum of interior angles of same side of the
transversal $= 180^{\circ}$

$\Rightarrow 2 x - 9 + 3 x - 7 = 180$

$\Rightarrow 5 x - 16 = 180$

$\Rightarrow 5 x = 180 + 16$

$\Rightarrow 5 x = 196$

$x = \frac{196}{5}$

$∴ x = 39.2$

Therefore, $2 x - 9 = (2 \times 39.2) - 9$
$= 78.4 - 9$
$= {69.4}^{\circ}$
$3 x - 7 = (3 \times 39.2) - 7$
$= 117.6 - 7$
$= {110.6}^{\circ}$
Hence, measure of each angle is ${69.4}^{\circ}$ and ${110.6}^{\circ}$

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Two parallel lines l and m are cut by a transversal t. If the interior angles on the same side of the transversal t be 2x−9 and 3x−7 . Find the measure of each angle.

Two parallel lines $l$ and $m$ are cut by a transversal $t$ . If the interior angles on the same side of the transversal $t$ be $2 x - 9$ and $3 x - 7$ . Find the measure of each angle.