In the given figure $m ∥ n$ and 'p' is a transversal . If $∠ 1 = 4 x + 5$ and $∠ 2 = 6 x - 15$ then find the angles.

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Solution

From figure,
$∠ 2 = ∠ 3$ ------corresponding angles
$∠ 3 = ∠ 1$ ------ vertically opposite angles

$∴ ∠ 1 = ∠ 2$
Given, $∠ 1 = 4 x + 5$ and $∠ 2 = 6 x - 15$
$⟹ 4 x + 5 = 6 x - 15$
$6 x - 4 x = 15 + 5$
$2 x = 20$
$⟹ x = 10$

$∴ ∠ 1 = 4 x + 5 = 4 (10) + 5 = 45^{\circ}$
and $∠ 2 = 6 x - 15 = 6 (10) - 15 = 45^{\circ}$

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In the given figure m∥n and 'p' is a transversal . If ∠1=4x+5 and ∠2=6x−15 then find the angles.

From figure,∠2=∠3 ------corresponding angles∠3=∠1 ------ vertically opposite angles∴∠1=∠2Given, ∠1=4x+5 and ∠2=6x−15⟹4x+5=6x−156x−4x=15+52x=20⟹x=10∴∠1=4x+5=4(10)+5=45∘and ∠2=6x−15=6(10)−15=45∘

In the given figure $m ∥ n$ and 'p' is a transversal . If $∠ 1 = 4 x + 5$ and $∠ 2 = 6 x - 15$ then find the angles.