Download App

Quadrilaterals — MATHS STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9MATHSQuadrilaterals1 Mark
Question
In a quadrilateral ABCD, $\angle\text{A} + \angle\text{C}$ is 2 times $\angle\text{B} + \angle\text{D}.$ If $\angle\text{A} = 140^\circ$ and $\angle\text{D} = 60^\circ,$ then ZB = ?
✓

Answer

  1. 60º
    Solution:
    Given,
    ABCD is a parallelogram
    $\angle\text{A} + \angle\text{C} = 2(\angle\text{B} + \angle\text{D})$
    $\angle\text{A} = 40^\circ$
    $∵ \angle\text{A} + \angle\text{B} + \angle\text{C} + \angle\text{D} = 360^\circ$ [angle sum property of quadrilateral]
    $\Rightarrow \angle\text{A} + \angle\text{C} + \angle\text{B} + \angle\text{D} = 360^\circ$
    $⇒ 2(\angle\text{B} + \angle\text{D})+ \angle\text{B} + \angle\text{D} = 360^\circ$
    $⇒ 3(\angle\text{B} + \angle\text{D})= 360^\circ$
    $\Rightarrow\angle\text{B}+\angle\text{D}=\frac{360^\circ}{3}=120^\circ$
    $\because\ \angle\text{B}=60^\circ$ [given]
    $\therefore\ \angle\text{B}=120^\circ-60^\circ=60^\circ$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q" from Quadrilaterals→Quadrilaterals — all question types→MATHS STD 9 question papers→Rajasthan Board STD 9 question papers→Rajasthan Board question paper generator→

Similar questions

Into how many chapters was the famous treatise, 'The Elements' divided by Euclid?
→
Vertical cross-section of a right circular cylinder is always a:
→
In a frequency distribution, ogives are graphical representation of:
→
The linear equation 2x - 5y = 7 has:
→
Write the correct answer in the following :
If $49\text{x}^2 -\text{b}=\Big(7\text{x}+\frac{1}{2}\Big)\Big(7\text{x}-\frac{1}{2}\Big),$ the value of b is.
→
D, E, F are the mid-point of the sides BC, CA and AB respectively of $\triangle\text{ABC}.$ Then $\triangle\text{DEF}$ is congruent to triangle.
→
In a parallelogram ABCD, if $\angle\text{DAB}=75^\circ$ and $\angle\text{DBC}=60^\circ,$ then $\angle\text{BDC}=$
  1. 75°
  2. 60°
  3. 45°
  4. 55°
→
If p(x) = x + 3, then p(x) + p(-x) is equal to:
→
Any solution of the linear equation 2x + 0y + 9 = 0 in two variables is of the form:
→
A point of the form (0, b) lies on:
→