SolveItNCERT · CBSE Boards

NCERT Exemplar · Class 9 Mathematics Quadrilaterals

56 questions · 56 still being checked

EXERCISE 8.2 11–14 (part 4 of 7)

  1. Exercise 11

    Can all the angles of a quadrilateral be acute angles? Give reason for your answer.

    Matches the book, not yet reviewed

    This working reaches the answer NCERT prints. It has not yet been read through by hand.

    NCERT’s answer
    No; Angle sum of a quadrilateral is $\displaystyle 360$°.
    \[\angle A + \angle B + \angle C + \angle D = 360^\circ \quad \text{(angle sum of a quadrilateral)} \]If all four angles are acute, each is less than \(\displaystyle 90^\circ\), so:\[\angle A + \angle B + \angle C + \angle D < 360^\circ \]This contradicts the angle sum, so no quadrilateral can have all four angles acute.Answer: No.

  2. Exercise 12

    Can all the angles of a quadrilateral be right angles? Give reason for your answer.

    Matches the book, not yet reviewed

    This working reaches the answer NCERT prints. It has not yet been read through by hand.

    NCERT’s answer
    Yes, Angle sum of a quadrilateral is $\displaystyle 360$°.
    \[\angle A + \angle B + \angle C + \angle D = 360^\circ \quad \text{(angle sum of a quadrilateral)} \]If each angle equals \(\displaystyle 90^\circ\):\[4 \times 90^\circ = 360^\circ \]which satisfies the angle sum, so a quadrilateral (e.g. a rectangle) can have all four angles right angles.Answer: Yes.

  3. Exercise 13

    Diagonals of a quadrilateral ABCD bisect each other. If ∠A=35∘\displaystyle \angle \mathrm{A}=35^{\circ}, determine ∠B\displaystyle \angle \mathrm{B}.

    Matches the book, not yet reviewed

    This working reaches the answer NCERT prints. It has not yet been read through by hand.

    NCERT’s answer
    $\displaystyle 145$°
    NCERT_Solution_Class9_Maths_Exemplar_Ch8_Ex8-2_Q13\[OA = OC, \quad OB = OD \quad \text{(diagonals bisect each other)} \]Diagonals bisecting each other make \(\displaystyle ABCD\) a parallelogram.\[\angle A + \angle B = 180^\circ \quad \text{(adjacent angles of a parallelogram)} \] \[35^\circ + \angle B = 180^\circ \] \[\angle B = 145^\circ \]Answer: \(\displaystyle \angle B = 145^\circ\).

  4. Exercise 14

    Opposite angles of a quadrilateral ABCD are equal. If AB=4 cm\displaystyle \mathrm{AB}=4 \mathrm{~cm}, determine CD.

    Matches the book, not yet reviewed

    This working reaches the answer NCERT prints. It has not yet been read through by hand.

    NCERT’s answer
    $\displaystyle 4$ cm
    NCERT_Solution_Class9_Maths_Exemplar_Ch8_Ex8-2_Q14\[\angle A = \angle C, \quad \angle B = \angle D \quad \text{(given)} \]Both pairs of opposite angles equal \(\displaystyle \Rightarrow\) \(\displaystyle ABCD\) is a parallelogram.\[CD = AB \quad \text{(opposite sides of a parallelogram)} \] \[CD = 4\ \text{cm} \]Answer: \(\displaystyle CD = 4\) cm.