In $□ A B C D$ , side $A B$ is parallel to side $D C$ . If $∠ A : ∠ D = 1 : 2$ and $∠ C : ∠ B = 4 : 5$ . Calculate smallest angle of the quadrilateral.

90^{\circ}

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80^{\circ}

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30^{\circ}

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60^{\circ}

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Solution

The correct option is D $60^{\circ}$
Since $A B$ and $D C$ are parallel $∠ A + ∠ D = 180^{\circ}$
$\Rightarrow ∠ A = 60^{\circ}$ and $∠ B = 120^{\circ}$
Also, $∠ C + ∠ B = 180^{\circ}$
$\Rightarrow ∠ C = 80^{\circ}$ and $∠ B = 100^{\circ}$
So, Option (D)

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In □ABCD, side AB is parallel to side DC. If ∠A:∠D=1:2 and ∠C:∠B=4:5. Calculate smallest angle of the quadrilateral.

The correct option is D 60∘Since AB and DC are parallel ∠A+∠D=180∘⇒∠A=60∘ and ∠B=120∘Also, ∠C+∠B=180∘⇒∠C=80∘ and ∠B=100∘So, Option (D)

In $□ A B C D$ , side $A B$ is parallel to side $D C$ . If $∠ A : ∠ D = 1 : 2$ and $∠ C : ∠ B = 4 : 5$ . Calculate smallest angle of the quadrilateral.

The correct option is D $60^{\circ}$
Since $A B$ and $D C$ are parallel $∠ A + ∠ D = 180^{\circ}$
$\Rightarrow ∠ A = 60^{\circ}$ and $∠ B = 120^{\circ}$
Also, $∠ C + ∠ B = 180^{\circ}$
$\Rightarrow ∠ C = 80^{\circ}$ and $∠ B = 100^{\circ}$
So, Option (D)