Question
ABCD is a parallelogram in which $\angle\text{A}=70^\circ$, compute $\angle\text{B},\angle\text{C}$ and $\angle\text{D}$.
✓
Answer
In parallelogram ABCD,
$\angle\text{A}=70^\circ$
But $\angle\text{A}+\angle\text{B}=180^\circ$ (Sum of adjacent angles)
$\Rightarrow70^\circ+\angle\text{B}=180^\circ$
$\Rightarrow\angle\text{B}=180^\circ-70^\circ=110^\circ$
$\angle\text{B}=110^\circ$
But $\angle\text{C}=\angle\text{A}$ and $\angle\text{D}=\angle\text{B}$ (Opposite angles)
$\angle\text{C}=70^\circ$ and $\angle\text{D}=110^\circ$
Hence,
$\angle\text{B}=110^\circ$
$\angle\text{C}=70^\circ$
and
$\angle\text{D}=110^\circ$
$\angle\text{A}=70^\circ$
But $\angle\text{A}+\angle\text{B}=180^\circ$ (Sum of adjacent angles)
$\Rightarrow70^\circ+\angle\text{B}=180^\circ$
$\Rightarrow\angle\text{B}=180^\circ-70^\circ=110^\circ$
$\angle\text{B}=110^\circ$
But $\angle\text{C}=\angle\text{A}$ and $\angle\text{D}=\angle\text{B}$ (Opposite angles)
$\angle\text{C}=70^\circ$ and $\angle\text{D}=110^\circ$
Hence,
$\angle\text{B}=110^\circ$
$\angle\text{C}=70^\circ$
and
$\angle\text{D}=110^\circ$
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
A playground has the shape of a rectangle, with two semi-circles on its smaller sides as diameters, added to its outside. If the sides of the rectangle are 36m and 24.5m, find the area of the playground. $\Big(\text{Take }\pi=\frac{22}{7}\Big )$
→The following histogram shows the monthly wages (in Rs.) of workers in a factory:
- In which wage-group the largest number of workers are being kept? What is their number?
- What wages are the least number of workers getting? What is the number of such workers?
- What is the total number of workers?
- What is the factory size?
Find (x + y) ÷ (x − y), if
$\text{x}=\frac{1}{4},\text{y}=\frac{3}{2}$
→$\text{x}=\frac{1}{4},\text{y}=\frac{3}{2}$
6400 workers were employed to construct a river bridge in four years. At the end of the first year, 25% workers were retrenched. At the end of the second year, 25% of those working at that time were retrenched. However, to complete the project in time, the number of workers was increased by 25% at the end of the third year. How many workers were working during the fourth year?
Factorize :
20x² – 26x + 8
Abhay borrowed Rs. 16000 at $7\frac{1}{2}\%$ per annum simple interest. On the same day, he lent it to Gurmeet at the same rate but compounded annually. What does he gain at the end of 2 years?
→Draw a circle of radius 28mm. Draw any one triangle and draw a trapezium on the graph paper. Find the area of these figures by counting the number of small squares on the graph paper. Verify your answers using formula for area of these figures.Observe that smaller the squares of graph paper, better is the approximation of area.
A and B can do a piece of work in 12 days, B and C in 15 days and C and A in 20 days. How much time will A alone take to finish the job?
Construct BARC such that l(BA) = l(BC) = 4.2 cm, l(AC) = 6.0 cm, l(AR) = l(CR) = 5.6 cm
Express product as a monomials and verify the result in each case for $x =1$ :
$\left(x^2\right)^3 \times(2 x) \times(-4 x) \times(5)$
→$\left(x^2\right)^3 \times(2 x) \times(-4 x) \times(5)$