Question
In the given figure, compute the value of x.
✓
Answer
In the given figure, $\angle\text{DCB}=45^\circ,\angle\text{CBA}=35^\circ$ and $\angle\text{BAD}=35^\circ$
Here, we will produce AD to meet BC at E
Now, using angle sum property of the triangle
In $\triangle\text{AEB}$
$\angle\text{BAE}+\angle\text{AEB}+\angle\text{EBA}=180^\circ$
$\angle\text{AEB}+35^\circ+45^\circ=180^\circ$
$\angle\text{AEB}+180^\circ=180^\circ$
$\angle\text{AEB}=180^\circ-80^\circ$
$\angle\text{AEB}=100^\circ$
Eurther, BEC is a straight line. So, using the property, "the angles forming a linear pair are supplementary", we get
$\angle\text{AEB}+\angle\text{AEC}=180^\circ$
$100^\circ+\angle\text{AEC}=180^\circ$
$\angle\text{AEC}=180^\circ-100^\circ$
$\angle\text{AEC}=80^\circ$
Also, using the property, " an exterior angle of a triangle is equal to the sum of its two opposite interior angles"
In $\triangle\text{DEC},\text{x}$ is its exterior angle
Thus,
$\angle\text{x}=\angle\text{DCE}+\angle\text{DEC}$
$=50^\circ+80^\circ$
$=130^\circ$
Therefore, $\text{x}=130^\circ.$
Here, we will produce AD to meet BC at E
Now, using angle sum property of the triangle
In $\triangle\text{AEB}$
$\angle\text{BAE}+\angle\text{AEB}+\angle\text{EBA}=180^\circ$
$\angle\text{AEB}+35^\circ+45^\circ=180^\circ$
$\angle\text{AEB}+180^\circ=180^\circ$
$\angle\text{AEB}=180^\circ-80^\circ$
$\angle\text{AEB}=100^\circ$
Eurther, BEC is a straight line. So, using the property, "the angles forming a linear pair are supplementary", we get
$\angle\text{AEB}+\angle\text{AEC}=180^\circ$
$100^\circ+\angle\text{AEC}=180^\circ$
$\angle\text{AEC}=180^\circ-100^\circ$
$\angle\text{AEC}=80^\circ$
Also, using the property, " an exterior angle of a triangle is equal to the sum of its two opposite interior angles"
In $\triangle\text{DEC},\text{x}$ is its exterior angle
Thus,
$\angle\text{x}=\angle\text{DCE}+\angle\text{DEC}$
$=50^\circ+80^\circ$
$=130^\circ$
Therefore, $\text{x}=130^\circ.$
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
100 surnames were randomly picked up from a local telephone directory and frequency distribution of the number of letters in the English alphabet in the surnames was found as follows:
| Number of letters | 1-4 | 4-6 | 6-8 | 8-12 | 12-20 |
| Number of surnames | 6 | 30 | 44 | 16 | 4 |
- Draw a histogram to depict the given information.
- Write the class interval in which the maximum number of surnames lie.
The total surface area of a solid cylinder is 231cm2 and its curved surface area is $\frac{2}{3}$ of the total surface area. Find the volume of the cylinder.
→Prove that the line segments joining the middle points of the sides of a triangle divide it into four congruent triangles.
The numbers 50, 42, 35, (2x + 10), (2x - 8), 12, 11, 8 have been written in a descending order. If their median is 25, find the value of x.
Draw the graph of the equation, 2x + y = 6.
Find the coordinates of the point where the graph cuts the x-axis.
Find the coordinates of the point where the graph cuts the x-axis.
An iron pillar consists of a cylindrical portion 2.8m high and 20cm in diameter and a cone 42cm high is surmounting it. Find the weight of the pillar, given that 1cm3 of iron weighs 7.5g. $\Big(\text{Use}\ \pi=\frac{22}{7}\Big).$
→In the given figure, ABCD is a square and $\angle\text{PQR}=90^{\circ}.$ If PB = QC = DR, prove that:
→- QB = RC,
- PQ = QR,
- $\angle\text{QPR}=45^{\circ}$
If two lines intersect, prove that the vertically opposite angles are equal.
Construct a histogram for the following frequency distribution:
| Class interval | 5-12 | 13-20 | 21-28 | 29-36 | 37-44 | 45-52 |
| Frequency | 6 | 15 | 24 | 18 | 4 | 9 |
Following table gives the distribution of students of sections A and B of a class according to the marks obtained by them.
Represent the marks of the students of both the sections on the same graph by two frequency polygons.What do you observe?
| Section A | Section B | ||||||||||||||||||||||||||
| Marks | Frequency | Marks | Frequency | ||||||||||||||||||||||||
|
|
|
| ||||||||||||||||||||||||