Question
In $\triangle \text{ABC}, \angle \text{ABC}=100^\circ, \angle \text{BAC}=35^\circ$ and $\text{BD}\bot \text{AC}$ meets side AC in D. If BD = 2cm, find $\angle \text{C},$ and length DC.
✓
Answer
We know that the sum of all angles of a triangle is 180°
Therefore, for the given $\triangle \text{ABC},$ we can say that:
$\angle \text{ABC}+\angle \text{BAC}+\angle \text{ACB}=180^\circ$
$100^\circ+35^\circ+\angle \text{ACB}=180^\circ$
$\angle \text{ACB}=180^\circ-135^\circ$
$\angle \text{ACB}=45^\circ$
$\angle \text{C}=45^\circ$
If we apply the above rule on $\triangle \text{BCD},$ we can say that:
$\angle \text{BCD}+\angle \text{BDC}+\angle \text{CBD}=180^\circ$
$45^\circ+90^\circ+\angle \text{CBD}=180^\circ$ $(\angle \text{ACD}=\angle \text{BCD}$ and BD parallel to AC$)$
$\angle \text{CBD}=180^\circ-135^\circ$
$\angle \text{CBD}=45^\circ$
We know that the sides opposite to equal angles have equal length.
Thus, BD = DC
DC = 2cm
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
Rakesh has a rectangular field of length 80m and breadth 60m. In it, he wants to make a garden 10m long and 4m broad at one of the corners and at another corner, he wants to grow flowers in two floor-beds each of size 4m by 1.5m. In the remaining part of the field, he wants to apply manures. Find the cost of applying the manures at the rate of Rs. 300 per area.
A 15m long ladder is placed against a wall to reach a window 12m high. Find the distance of the foot of the ladder from the wall.
A dice is thrown 100 times and the outcomes are noted as given below:
When a dice is thrown at random, what is the probability of getting a (i) 3, (ii) 6, (iii) 6, (iv) 1?
|
Outcome
|
1
|
2
|
3
|
4
|
5
|
6
|
|
Frequency
|
21
|
14
|
18
|
15
|
23
|
9
|
The length of a side of a square field is 4m. What will be the altitude of the rhombus, if the area of the rhombus is equal to the square field and one of its diagonals is 2m?
The radius of one circular field is 5m and that of the other is 13m. Find the radius of the circular field whose area is the difference of the areas of first and second field.
A rectangular grassy lawn measuring 38 m by 25 m has been surrounded externally by a 2.5 -m-wide path. Calculate the cost of gravelling the path at the rate of Rs 120 per $m ^2$.
→The following table shows the marks obtained by 41 students of a class.
Find the median and mean marks.
Using empirical formula, calculate its mode.
| Marks obtained | 15 | 17 | 20 | 22 | 25 | 30 |
| Number of students | 2 | 5 | 10 | 12 | 8 | 4 |
Using empirical formula, calculate its mode.
How many envelopes can be made out of a sheet of paper 125cm by 85cm; supposing one envelope requires a piece of paper of size 17cm by 5cm?
Explain the concept of interior and exterior angle and in the figures given below. Find x and y.
Solve the following equations. Check your result in case.
$\frac{\text{x}-2}{4}+\frac{1}{3}=\text{x}-\frac{2\text{x}-1}{3}$
→$\frac{\text{x}-2}{4}+\frac{1}{3}=\text{x}-\frac{2\text{x}-1}{3}$