If angle 1- - x and angle 7- - displaystyle frac -2-3- x- then angle 5 is equal to 36-circ-108-circ-72-circ-144-circ-

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Toppr Admin · Accepted Answer

-x2220-5-x2220-1-x-xA0-Corresponding angles-x2220-5-x2220-7-180-x2218-xA0-Linear pair-x-23x-180-x2218-x21D2-5x3-180-x2218-x21D2-x-180-x2218-5-180-x2218-x2234-x2220-5-108-x2218-

If $∠ 1 = x$ and $∠ 7 = \frac{2}{3} x$ , then $∠ 5$ is equal to

$36^{\circ}$
$108^{\circ}$
$72^{\circ}$
$144^{\circ}$

$∠ 5 = ∠ 1 = x$ (Corresponding angles)
$∠ 5 + ∠ 7 = 180^{\circ}$ (Linear pair)
$x + \frac{2}{3} x = 180^{\circ} \Rightarrow \frac{5 x}{3} = 180^{\circ}$
$\Rightarrow x = \frac{180^{\circ}}{5} = 180^{\circ}$
$∴ ∠ 5 = 108^{\circ}$

If ∠1=x and ∠7=23x, then ∠5 is equal to 36∘108∘72∘144∘

∠5=∠1=x (Corresponding angles)∠5+∠7=180∘ (Linear pair)x+23x=180∘⇒5x3=180∘⇒x=180∘5=180∘∴∠5=108∘

If $∠ 1 = x$ and $∠ 7 = \frac{2}{3} x$ , then $∠ 5$ is equal to

$36^{\circ}$
$108^{\circ}$
$72^{\circ}$
$144^{\circ}$

$∠ 5 = ∠ 1 = x$ (Corresponding angles)
$∠ 5 + ∠ 7 = 180^{\circ}$ (Linear pair)
$x + \frac{2}{3} x = 180^{\circ} \Rightarrow \frac{5 x}{3} = 180^{\circ}$
$\Rightarrow x = \frac{180^{\circ}}{5} = 180^{\circ}$
$∴ ∠ 5 = 108^{\circ}$