In quadrilateral ABCD- if - A -60- and - B - - C - - D -2- 4- 6- then find the measure of - C-A- 90-B- 100-C -110-D- 120-

The correct option is B 100^∘Let ∠ B=2x, nbsp;∠ C=4x and ∠ D=6x ∵ Sum o angles in a quadrilateral is 360^∘ ∴∠ A+∠ B+∠ C+∠ D=360^∘ ⇒ 60^∘+2x+4x+6x=360^∘ ⇒ 12x ...

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Byju's Answer

Standard IX

Mathematics

Angle Sum Property of a Quadrilateral

In quadrilate...

Question

In quadrilateral ABCD, if $∠ A = 60^{\circ}$ and $∠ B : ∠ C : ∠ D = 2 : 4 : 6$ , then find the measure of $∠ C .$

90^{\circ}

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100^{\circ}

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110^{\circ}

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120^{\circ}

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Solution

The correct option is B $100^{\circ}$
Let $∠ B = 2 x, ∠ C = 4 x a n d ∠ D = 6 x$
$∵$ Sum o angles in a quadrilateral is 360 $^{\circ}$
$∴ ∠ A + ∠ B + ∠ C + ∠ D = 360^{\circ}$
$\Rightarrow 60^{\circ} + 2 x + 4 x + 6 x = 360^{\circ}$
$\Rightarrow 12 x = 360^{\circ} - 60^{\circ}$
$\Rightarrow 12 x = 300^{\circ}$
$\Rightarrow x = 25^{\circ}$
So,
$∠ C = 4 x = 4 \times 25^{\circ} = 100^{\circ}$

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In quadrilateral ABCD, if ∠ A=60∘ and ∠ B:∠ C:∠ D=2:4:6, then find the measure of ∠ C.

The correct option is B 100∘Let ∠ B=2x,∠ C=4x and ∠ D=6x ∵ Sum o angles in a quadrilateral is 360∘ ∴∠ A+∠ B+∠ C+∠ D=360∘ ⇒60∘+2x+4x+6x=360∘ ⇒12x=360∘−60∘ ⇒12x=300∘ ⇒x=25∘ So, ∠ C=4x=4×25∘=100∘

In quadrilateral ABCD, if $∠ A = 60^{\circ}$ and $∠ B : ∠ C : ∠ D = 2 : 4 : 6$ , then find the measure of $∠ C .$