Quadrilateral and Parallelogram Solved Extra Questions ~ SCC Education

Tuesday, 22 March 2016

Quadrilateral and Parallelogram Solved Extra Questions

Author: scceducation | March 22, 2016 | No Comments |

Mathematics ,Number System,scc,ssc,scceducation,test paper,Test paper ,expotential,

Quadrilateral and Parallelogram Solved Extra Questions:-

1. Prove that any two adjacent angles of a parallelogram are supplementary

Solution: Let ABCD be a parallelogram

Then, AD ∥ BC and AB is a transversal.

Therefore, A + B = 180°

[Since, sum of the interior angles on the same side of the transversal is 180°]

Similarly, ∠B + ∠C = 180°, ∠C + ∠D = 180° and ∠D + ∠A = 180°.

Thus, the sum of any two adjacent angles of a parallelogram is 180°.

Hence, any two adjacent angles of a parallelogram are supplementary

2. Two adjacent angles of a parallelogram are as 2 : 3. Find the measure of each of its angles.

Solution: Let ABCD be a given parallelogram

Then, ∠A and ∠B are its adjacent angles.

Let ∠A = (2x)° and ∠B = (3x)°. Then, ∠A + ∠B = 180°

[Since, sum of adjacent angles of a ∥gm is 180°] ⇒ 2x + 3x = 180 ⇒ 5x = 180 ⇒ x = 36. Therefore, ∠A = (2 × 36)° = 72° and ∠B = (3 × 36°) = 108°. Also, ∠B + ∠C = 180°

[Since, ∠B and ∠C are adjacent angles] = 108° + ∠C = 180° [Since, ∠B = 108°] ∠C = (180° - 108°) = 72°. Also, ∠C + ∠D = 180° [Since, ∠C and ∠D are adjacent angles]

72° + ∠D = 180° ⇒ ∠D = (180° - 72°) 108°.

Therefore, ∠A = 72°, ∠B = 108°, ∠C = 72°and ∠D = 108°.

To read this complete topic click here.........