Question
In the adjoining figure, ABCD is a parallelogram in which $\angle\text{A}=70^{\circ}.$ Calculate $\angle\text{B},\angle\text{C}$ and $\angle\text{D}.$
✓
Answer
In a parallelogram, opposite angles are equal.$\therefore\angle\text{A}=\angle\text{C}=72^{\circ}$The sum of all the four angles of a parallelogram is 360° So, $\angle\text{A}+\angle\text{B}+\angle\text{C}+\angle\text{D}=360^{\circ}$$\Rightarrow72^{\circ}+\angle\text{B}+72^{\circ}+\angle\text{D}=360^{\circ}$ $[\because\angle\text{A} = \angle\text{C}]$
$\Rightarrow2\angle\text{B}+144^{\circ}=360^{\circ}$ $[\because\angle\text{B}=\angle\text{D}]$
$\Rightarrow2\angle\text{B}=360^{\circ}-144^{\circ}=216{^\circ}$
$\Rightarrow\angle\text{B}=\frac{216}{2}=108^{\circ}$
$\therefore\angle\text{B}=108^{\circ},\angle\text{C}=72^{\circ}$ and $\angle\text{D}=108^{\circ}.$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
In Q.No. 7, what is the probability of getting at least two heads?
$x^4 - 2x^3 - 7x^2 + 8x + 12.$
→Explain the reading and interpretation of bar graphs.
Read the bar graph shown in the figure and answer the following questions:
- What is the information given by the bar graph?
- How many tickets of Assam State Lottery were sold by the agent?
- Of which state, were the maximum number of tickets sold?
- State whether true or false.
- Of which state were the minimum numbers of tickets sold?
The bisectors of base angles of a triangle cannot enclose a right angle in any case.
Simplify:
$(2x + p - c)^2 - (2x - p + c)^2$
→$(2x + p - c)^2 - (2x - p + c)^2$
The perimeter of a triangular field is 540m and its sides are in the ratio $25 : 17 : 12$. Find the area of triangle.
→In the given figure, line RP || line MS and line DK is their transversal. ∠DHP = 85°. Find the measures of following angles.
i. ∠RHD
ii. ∠PHG
iii. ∠HGS
iv. ∠MGK
How many cubic meters of earth must be dug out to sink a well 21 m deep and 6 m diameter?
Find the cost of plastering the inner surface as well at ₹ 9.50 per $m ^2$.
→Find the cost of plastering the inner surface as well at ₹ 9.50 per $m ^2$.
In the given figure, O is the center of the circle. If $\angle\text{CEA}=30^\circ,$ find the value of x, y and z.
→