Question
In a parallelogram ABCD, if $\angle\text{A}=(3\text{x}-20)^\circ,\angle\text{B}=(\text{y}+15)^\circ,\angle\text{C}=(\text{x}+40)^\circ,$ then find the values of x and y.
✓
Answer
In parallelogram ABCD, $\angle\text{A}$ and $\angle\text{C}$ are opposite angles. We know that in a parallelogram, the opposite angles are equal. Therefore,$\angle\text{C}=\angle\text{A}$
We have $\angle\text{A}=(3\text{x}-20)^\circ$ and $\angle\text{C}=(\text{x}+40)^\circ$ Therefore, x + 40º = 3x - 20º x - 3x = -40º - 20º -2x = -60º x = 30º Therefore,$\angle\text{A}=(3\text{x}-20)^\circ$
$\angle\text{A}=[3(30)-20]^\circ$
$\angle\text{A}=70^\circ$
Similarly,$\angle\text{C}=70^\circ$
Also, $\angle\text{B}=(\text{y}+15)^\circ$ Therefore,$\angle\text{D}=\angle\text{B}$
$\angle\text{D}=(\text{y}+15)^\circ$
By angle sum property of a quadrilateral, we have:$\angle\text{A}+\angle\text{B}+\angle\text{C}+\angle\text{D}=360^\circ$
$70^\circ+(\text{y}+15)^\circ+70^\circ+(\text{y}+15)^\circ=360^\circ$
$140^\circ+2(\text{y}+15)^\circ=360^\circ$
$2(\text{y}+15)^\circ=360^\circ-140^\circ$
$2(\text{y}+15)^\circ=220^\circ$
$(\text{y}+15)^\circ=110^\circ$
$\text{y}=95^\circ$
Hence the required values for x and y are 30º and 95º respectively.
We have $\angle\text{A}=(3\text{x}-20)^\circ$ and $\angle\text{C}=(\text{x}+40)^\circ$ Therefore, x + 40º = 3x - 20º x - 3x = -40º - 20º -2x = -60º x = 30º Therefore,$\angle\text{A}=(3\text{x}-20)^\circ$
$\angle\text{A}=[3(30)-20]^\circ$
$\angle\text{A}=70^\circ$
Similarly,$\angle\text{C}=70^\circ$
Also, $\angle\text{B}=(\text{y}+15)^\circ$ Therefore,$\angle\text{D}=\angle\text{B}$
$\angle\text{D}=(\text{y}+15)^\circ$
By angle sum property of a quadrilateral, we have:$\angle\text{A}+\angle\text{B}+\angle\text{C}+\angle\text{D}=360^\circ$
$70^\circ+(\text{y}+15)^\circ+70^\circ+(\text{y}+15)^\circ=360^\circ$
$140^\circ+2(\text{y}+15)^\circ=360^\circ$
$2(\text{y}+15)^\circ=360^\circ-140^\circ$
$2(\text{y}+15)^\circ=220^\circ$
$(\text{y}+15)^\circ=110^\circ$
$\text{y}=95^\circ$
Hence the required values for x and y are 30º and 95º respectively.
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 the adjoining figure, ABCD is a parallelogram in which AB is produced to E so that BE = AB. Prove that ED bisects BC.
Find the value of a, if $x + 2$ is a factor of $4x^4 + 2x^3 - 3x^2 + 8x + 5a$.
→Calculate the mean for the following distribution:
|
x:
|
5
|
6
|
7
|
8
|
9
|
|
f:
|
4
|
8
|
14
|
11
|
3
|
Following data gives the number of children in 40 families:
1, 2, 6, 5, 1, 5, 1, 3, 2, 6, 2, 3, 4, 2, 0, 0, 4, 4, 3, 2, 2, 0, 0, 1, 2, 2, 4, 3, 2, 1, 0, 5, 1, 2, 4, 3, 4, 1, 6, 2, 2.
Represent it in the form of a frequency distribution.
1, 2, 6, 5, 1, 5, 1, 3, 2, 6, 2, 3, 4, 2, 0, 0, 4, 4, 3, 2, 2, 0, 0, 1, 2, 2, 4, 3, 2, 1, 0, 5, 1, 2, 4, 3, 4, 1, 6, 2, 2.
Represent it in the form of a frequency distribution.
Radius of circle is $10\ cm$ . There are two chords of length $16\ cm$ each. What will be the distance of these chords from the centre of the circle?
Given: In a circle with centre O ,
OR and OP are radii and RS and PQ are its congruent chords.
$P Q=R S=16 cm$
$O R=O P=10 cm$
seg $OU \perp$ chord PQ, P-U-Q
seg $OT \perp$ chord RS, R-T-S
To find: Distance of chords from centre of the circle.
→Given: In a circle with centre O ,
OR and OP are radii and RS and PQ are its congruent chords.
$P Q=R S=16 cm$
$O R=O P=10 cm$
seg $OU \perp$ chord PQ, P-U-Q
seg $OT \perp$ chord RS, R-T-S
To find: Distance of chords from centre of the circle.
Visualize the representation of $4.\overline{67}$ on the number line up to 4 decimal places.
→Construct a frequency table with equal class intervals from the following data on the monthly wages (in rupees) of 28 laborers working in a factory, taking one of the class intervals as 210-230 (230 not included).
220, 268, 258, 242, 210, 268, 272, 242, 311, 290, 300, 320, 319, 304, 302, 218, 306, 292, 254, 278, 210, 240, 280, 316, 306, 215, 256, 236.
220, 268, 258, 242, 210, 268, 272, 242, 311, 290, 300, 320, 319, 304, 302, 218, 306, 292, 254, 278, 210, 240, 280, 316, 306, 215, 256, 236.
In a $\triangle\text{ABC},$ it is given that $\angle\text{A}:\angle\text{B}:\angle\text{C}=3:2:1$ and $\text{CD}\perp\text{AC}.$ Find $\angle\text{ECD}.$
→The mean salary of 20 workers is ₹10,250. If the salary of office superintendent is added, the mean will increase by ₹ 750. Find the salary of the office superintendent.
In figure, $\angle\text{AOC}$ and $\angle\text{BOC}$ from a linear pair. If a - 2b = 30°, find a and b.
→