Question
In the following figure, BA is parallel to CD. Find the angles a, b and c:
✓
Answer
In the given figure,
ABC is a triangle and CD || BA, BC is produced to E.
∠A = 60°, ∠B = 70°
∵ AB || DC and BE is its transversal
∴ ∠DCE = ∠ABC (Corresponding angles)
⇒ a = 70°
∴ a = 70°
Similarly, AB || DC and AC is its transversal
∴ ∠ACD = ∠BAC (Alternate angles)
⇒ b = 60°
∴ b = 60°
But a + b + c = 180° (Straight line angle)
⇒ 70° + 60° + c = 180°
⇒ 130° + c = 180°
⇒ c = 180° - 130° = 50°
Hence a = 70°, b = 60° and c = 50°
ABC is a triangle and CD || BA, BC is produced to E.
∠A = 60°, ∠B = 70°
∵ AB || DC and BE is its transversal
∴ ∠DCE = ∠ABC (Corresponding angles)
⇒ a = 70°
∴ a = 70°
Similarly, AB || DC and AC is its transversal
∴ ∠ACD = ∠BAC (Alternate angles)
⇒ b = 60°
∴ b = 60°
But a + b + c = 180° (Straight line angle)
⇒ 70° + 60° + c = 180°
⇒ 130° + c = 180°
⇒ c = 180° - 130° = 50°
Hence a = 70°, b = 60° and c = 50°
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
Find the $L.C.M$. of the following group of numbers, using
→- the prime factor method and
- the common division method
Construct a triangle ABC, in which AB = AC = 5 cm and BC 6 cm. Draw all its lines of Symmetry.
When three consecutive natural numbers are added, the sum is 66, find the numbers.
A line segment AP stands at point P of a straight line BC such that ∠APB = 5x – 40° and ∠APC = .x+ 10°; find the value of x and angle APB.
Two opposite angles of a parallelogram are 100° each. Find each of the other two opposite angles.
Construct a triangle ABC given AB = 6 cm, BC = 5 cm and CA = 5.6 cm. From vertex A draw a perpendicular on to side BC. Measure the length of this perpendicular.
Arrange the given fractions in ascending order of magnitude:
$\frac{2}{3}, \frac{5}{9}, \frac{5}{6}, \frac{3}{8}$
→$\frac{2}{3}, \frac{5}{9}, \frac{5}{6}, \frac{3}{8}$
Use the information given in the following figure to find :
(i) x
(ii) ∠B and ∠C
(i) x
(ii) ∠B and ∠C
The sale of vehicles, in a particular city, during the first six months of the year 2016 is shown below:
Draw a pictograph to represent the above data.
| Month | Jan | Feb | March | April | May | June |
| Number of vehicles sold | 3000 | 2500 | 4000 | 1000 | 1500 | 3500 |
Evaluate:
$3 \frac{5}{6}-1 \frac{4}{15}-\left(3 \frac{2}{9}-1 \frac{3}{5}\right)$
→$3 \frac{5}{6}-1 \frac{4}{15}-\left(3 \frac{2}{9}-1 \frac{3}{5}\right)$