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Lesson Posted on 20 Aug Learn Class 9

Lines and angle for class 9 mathematics

Vikas Kumar

Five-year experience in teaching physics, mathematics to 6 to 11th standard students. Created several...

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Answered 2 days ago Learn Triangles

12. If the diagonals of the rectangle ABCD intersect at O and ∠COD = 78°, then ∠OAB is:

Debojit Sarkar

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Diagonals of a rectangle bisect each other and they are equal in length ∴Δ AOB will be an isosceles triangle with AO=BO In ΔAOB, ∠AOB = ∠COD ............. ∠OAB=∠OBA ................ ∴∠AOB +2∠OAB = 180° ⇒ 78º + 2∠OAB = 180° ⇒... read more

Diagonals of a rectangle bisect each other and they are equal in length

∴Δ AOB will be an isosceles triangle with AO=BO

In ΔAOB,

∠AOB = ∠COD .............[ Vertically opposite angles]

∠OAB=∠OBA ................[ Angle opposite to equal sides]

∴∠AOB +2∠OAB = 180°

⇒ 78º + 2∠OAB = 180°

⇒ ∠OAB = 51° [ Ans.]

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Answered 2 days ago Learn Triangles

13. The measure of an angle is twice the measure of supplementary angle. What is the measure of angles?

Debojit Sarkar

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Let the smaller angle is x°, the larger angle will be 2x°, ∴ 3x°= 180° ⇒x° = 60° ∴ smaller angle is 60° and larger angle is 120°
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Answered 3 days ago Learn Quadrilaterals

6. ABCD is a trapezium in which AB is parallel to CD. If ∟A = 36° and ∟B = 81°, then find ∟C and ∟D.

Debojit Sarkar

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Since ABCD is a trapezium, therefore, their consecutive angles will be supplementary. Hence, ∠A+∠D=180º and ∠B+∠C=180º. ⇒36º+∠D=180º and 81º+∠C=180º ⇒∠D=144º and ∠C=99º (Ans.)
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Answered 2 days ago Learn Quadrilaterals

8. In a parallelogram ABCD find the measure of all the angles if one angle measures 68°.

Debojit Sarkar

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In a parallelogram consecutive interior angles are supplementary, ∴If ∠A =68°, ∠B=(180°-68°)=112°, ∠C=68º, ∠D=112°
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Answered 2 days ago Learn Quadrilaterals

9. The lengths of diagonals of a rhombus are 24 cm and 18 cm respectively. Find the length of each side of the rhombus.

Debojit Sarkar

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Diagonals of a rhombus bisect each other perpendicularly, Let us consider a rhombus ABCD, having diagonals bisect at O, AC=24 cm, BD=18 cm, In right ΔABO, AO=12 cm, BO= 9 cm, ∴AB= √(12²+9²) =15 cm ∴ Length of each side of the rhombus is 15 cm. read more

Diagonals of a rhombus bisect each other perpendicularly,

Let us consider a rhombus ABCD, having diagonals bisect at O, AC=24 cm, BD=18 cm,

In right ΔABO,

AO=12 cm, BO= 9 cm, 

∴AB= √(12²+9²) =15 cm

∴ Length of each side of the rhombus is 15 cm. [Ans.]

 

 

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Answered 2 days ago Learn Quadrilaterals

10. In a parallelogram ABCD find the measure of all the angles if one its angles is 15° less than twice... read more
10. In a parallelogram ABCD find the measure of all the angles if one its angles is 15° less than twice the smallest angle. read less

Debojit Sarkar

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In a parallelogram adjacent angles are supplementary, Let ∠A=x°, then ∠B = 2x°-15 ⇒ x°+2x° -15° =180° ⇒ x° = 65° ∠A = 65°, ∠B = 115°, ∠C = 65° and ∠D = 115°
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Answered on 24 Aug Learn Triangles

1. Two adjacent angles on a straight line are in a ratio 5:4. Find the measure of each one of these angles.... read more
1. Two adjacent angles on a straight line are in a ratio 5:4. Find the measure of each one of these angles. (Answer: 100 ° and 80 °degree). read less

Vikas Rai

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100° &80°
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Answered on 24 Aug Learn Triangles

4. The angles of the triangle are in the ratio 2:3:7. Find the measure of each angle of the triangle.... read more
4. The angles of the triangle are in the ratio 2:3:7. Find the measure of each angle of the triangle. (Answer: 30°, 45° and 105°) read less

Vikas Rai

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30° 45° 105°
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Answered on 11 Aug Learn Construction

8. Construct an equilateral triangle whose perimeter is 16.2 cm.

Deepika Agrawal

"Balancing minds, one ledger at a time." "Counting on expertise to balance your knowledge."

Construct an equilateral triangle whose perimeter is 16.2 cm Draw a line BC = 5.4 cm. Using a compass, take radius 5.4 cm and using B as a centre draw an arc. Taking the same radius and using C as a centre, cut the previous arc at A. Join AB and AC. read more
Construct an equilateral triangle whose perimeter is 16.2 cm
  1. Draw a line BC = 5.4 cm.
  2. Using a compass, take radius 5.4 cm and using B as a centre draw an arc.
  3. Taking the same radius and using C as a centre, cut the previous arc at A.
  4. Join AB and AC.

construct an equilateral triangle whose perimeter is 16.2 cm ...

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