In a quadrilateral ABCD- the bisectors of - A and - B meet at E- If - C -75- and - D -125- then find the measure of - AEB-A- 90-B- 100-C- 110-D- 120-

The correct option is B 100^∘In quadrilateral ABCD, ∠ A+∠ B+∠ C+∠ D=360^∘ ⇒∠ A+∠ B+75^∘+125^∘=360^∘ ⇒∠ A+∠ B=360^∘ 200^∘ ⇒∠ A+∠ B=160^∘ Now in AEB, ∠ EAB+∠ AB ...

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Byju's Answer

Standard IX

Mathematics

Introduction to Quadrilaterals

In a quadrila...

Question

In a quadrilateral ABCD, the bisectors of $∠ A$ and $∠ B$ meet at E. If $∠ C = 75^{\circ}$ and $∠ D = 125^{\circ}$ , then find the measure of $∠ A E B$ .

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 $100^{\circ}$
In quadrilateral ABCD,

$∠ A + ∠ B + ∠ C + ∠ D = 360^{\circ}$
$\Rightarrow ∠ A + ∠ B + 75^{\circ} + 125^{\circ} = 360^{\circ}$
$\Rightarrow ∠ A + ∠ B = 360^{\circ} - 200^{\circ}$
$\Rightarrow ∠ A + ∠ B = 160^{\circ}$
Now in $△ A E B,$
$∠ E A B + ∠ A B E + ∠ A E B = 180^{\circ}$
$\Rightarrow \frac{1}{2} ∠ A + \frac{1}{2} ∠ B + ∠ A E B = 180^{\circ}$
$\Rightarrow \frac{1}{2} (∠ A + ∠ B) + ∠ A E B = 180^{\circ}$
$\Rightarrow \frac{1}{2} \times 160^{\circ} + ∠ A E B = 180^{\circ}$
$\Rightarrow ∠ A E B = 180^{\circ} - 80^{\circ}$
$\Rightarrow ∠ A E B = 100^{\circ}$

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In a quadrilateral ABCD, the bisectors of ∠ A and ∠ B meet at E. If ∠ C=75∘ and ∠ D=125∘, then find the measure of ∠ AEB.

In a quadrilateral ABCD, the bisectors of $∠ A$ and $∠ B$ meet at E. If $∠ C = 75^{\circ}$ and $∠ D = 125^{\circ}$ , then find the measure of $∠ A E B$ .