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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

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)

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)

physics-General

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In the figure, a block slides along a track from one level to a higher level, by moving through an intermediate valley. The track is frictionless untill the block reaches the higher level. There a frictional force stops the block in a distance d. The block's initial speed $v subscript 0 end subscript text is end text 6 m divided by s text , end text$ the height difference h is 1.1 m and the coefficient of kinetic friction $mu$ is 0.6. The value of d is

physics-General

A ball rolls down an inclined plane figure. The ball is first released from rest from P and then later from Q. Which of the following statement is/are correct?

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A wedge of mass M fitted with a spring of stiffness 'k' is kept on a smooth horizontal surface. A rod of mass m is kept on the wedge as shown in the figure. System is in equilibrium. Assuming that all surfaces are smooth, the potential energy stored in the spring is:

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A particle 'A' of mass $fraction numerator 10 over denominator 7 end fraction$ kg is moving in the positive x–direction. Its initial position is x = 0 & initial velocity is 1 $m divided by s$ . The velocity at $x equals 10 m$ is:(use the graph given)

A particle 'A' of mass $fraction numerator 10 over denominator 7 end fraction$ kg is moving in the positive x–direction. Its initial position is x = 0 & initial velocity is 1 $m divided by s$ . The velocity at $x equals 10 m$ is:(use the graph given)

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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

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

parallel

In figure, triangle ABC is right-angled at B. Given that AB = 9 cm, AC = 15 cm, calculate the length of BC

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

In figure, triangle ABC is right-angled at B. Given that AB = 9 cm, AC = 15 cm, calculate the length of BC

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

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

Hence AF=(1/3)AC

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Hence AF=(1/3)AC

In the figure shown below, $angle B equals angle C equals 65 to the power of ring operator end exponent$ and $angle D equals 35 to the power of ring operator end exponent$ . Which one of the following is a true statement?

Hence Choice 1 is correct

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Hence Choice 1 is correct

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Hence choice 4 is correct

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Hence choice 4 is correct

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Hence choice 2 is correct

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Hence choice 2 is correct

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In Figure. PS is the bisector of $angle Q P R$ and $P T perpendicular Q R$ . Then $angle T P S$ is equal to

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Two identical blocks A and B are placed on two inclined planes as shown in diagram. Neglect air resistance and other friction. Choose the correct statement:

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Statement II: Acceleration of 'A' will be greater than acceleration of 'B' when both are released to slide on inclined plane. Statement III: Work done by external agent to move block slowly from position B to O is negative

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Figure shows the roller coaster track. Each car will start from rest at point A and will roll with negligible friction. It is important that there should be at least some small positive normal force exerted by the track on the car at all points, otherwise the car would leave the track. With the above fact, the minimum safe value for the radius of curvature at point B is (g = 10 $m divided by s to the power of 2 end exponent$ ):

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