In a quadrilateral ABCD- - A-90- - B-3 x- - C-3 x-5- - D-8 x-15- Then the value of - D is

The correct option is C Since the sum of interior angles of a quadrilateral is 360^∘ 90+3x+3x+5+8x 15 = 360 90+14x 10=360 14x=360 80 =280 ⇒ x = 20 ∠D = ...

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Standard IX

Mathematics

Quadrilaterals

In a quadrila...

Question

In a quadrilateral ABCD, $∠ A = 90^{\circ}, ∠ B = 3 x, ∠ C = 3 x + 5, ∠ D = 8 x - 15$ . Then the value of $∠ D$ is

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Solution

The correct option is D

Since the sum of interior angles of a quadrilateral is $360^{\circ}$
$90 + 3 x + 3 x + 5 + 8 x - 15 = 360 90 + 14 x - 10 = 360 14 x = 360 - 80 = 280 \Rightarrow x = 20 ∠ D = 8 x - 15 = 8 (20) - 15 = 145^{\circ}$

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In a quadrilateral ABCD, ∠A=90∘,∠B=3x,∠C=3x+5,∠D=8x−15. Then the value of ∠D is

The correct option is D Since the sum of interior angles of a quadrilateral is 360∘ 90+3x+3x+5+8x−15=36090+14x−10=36014x=360−80=280⇒x=20∠D=8x−15=8(20)−15=145∘

In a quadrilateral ABCD, $∠ A = 90^{\circ}, ∠ B = 3 x, ∠ C = 3 x + 5, ∠ D = 8 x - 15$ . Then the value of $∠ D$ is

The correct option is D

Since the sum of interior angles of a quadrilateral is $360^{\circ}$
$90 + 3 x + 3 x + 5 + 8 x - 15 = 360 90 + 14 x - 10 = 360 14 x = 360 - 80 = 280 \Rightarrow x = 20 ∠ D = 8 x - 15 = 8 (20) - 15 = 145^{\circ}$