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Maths-

General

Easy

Question

In the adjoining figure, AP and BP are angle bisector of $angle A$ and $angle B$ which meets at P on the parallelogram ABCD. Then $2 angle A P B$ =

$∠ C + ∠ D$
$∠ A + ∠ C$
$∠ B + ∠ D$
$2 ∠ C$

hint Hint:

The correct answer is: $angle C plus angle D$

We should find value of $2 angle A P B space i n space t e r m s space o f space g i v e n space a n g l e s$
If AP and BP are angle bisector, then

$∠ 1 = ∠ 2 = ∠ A / 2 ∠ 3 = ∠ 4 = ∠ B / 2$

And Consecutive angles are supplementary

$∴ ∠ 1 + ∠ 2 = 180 - (∠ 3 + ∠ 4)$

$∠ A = 180 - ∠ B$

From the figure,

$∠ A P B = 180 - (∠ 1 + ∠ 3)$

$=>1 80 - (180 - (∠ 2 + ∠ 4))$

$=>∠ 2 + ∠ 4 = ∠ A / 2 + ∠ B / 2$

$\Rightarrow 2 ∠ A P B = ∠ A + ∠ B$

$Since in parallelogram ∠ A + ∠ B= ∠C + ∠D$

Hence option 1 is correct

Related Questions to study

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A block of mass m is attached with a massless spring of force constant k. The block is placed over a rough inclined surface for which the coefficient of friction is $mu equals 3 divided by 4$ . The minimum value of M required to move the block up the plane is:(Neglect mass of string and pulley and friction in pulley)

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The perimeter of a right triangle is 132 cm. and the sum of the squares of its sides is 6050 cm². What is the sum of the perpendicular sides –

Hence Choice 1 is correct

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Hence Choice 1 is correct

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For such questions, we should know the Pythagoras theorem of a triangle.

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In DABC, AD is the median through A and E is the produced meets in F figure. Then the value of AF is equal to

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Hence Choice 1 is correct

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