Download App

Linear Equations In Two Variables — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsLinear Equations In Two Variables5 Marks
Question
Find the angles of a cyclic quadrilateral ABCD in which:
$\angle\text{A}=(\text{4x}+20)^\circ,$ $\angle\text{B}=(\text{3x}-5)^\circ,$ $\angle\text{C}=(\text{4y})^\circ$ and $\angle\text{D}=(\text{7y}+5)^\circ.$
✓

Answer

Given:
In a cyclic quadrilateral ABCD, we have:
$\angle\text{A}=(4\text{x}+20)^\circ$
$\angle\text{B}=(3\text{x}-5)^\circ$
$\angle\text{C}=(4\text{y})^\circ$
$\angle\text{D}=(7\text{y}+5)^\circ$
$\angle\text{A}+\angle\text{C}=180^\circ$ and $\angle\text{B}+\angle\text{D}=180^\circ$ [Since ABCD is a cyclic quadrilateral]
Now, $\angle\text{A}+\angle\text{C}=(4\text{x}+20)^\circ+(4\text{y})^\circ=180^\circ$
⇒ 4x + 4y + 20 = 180
⇒ 4x + 4y = 180 - 20 = 160
⇒ x + y = 40 ....(i)
Also, $\angle\text{B}+\angle\text{D}=(3\text{x}-5)^\circ+(7\text{y}+5)^\circ=180^\circ$
⇒ 3x + 7y = 180 ...(ii)
On multiplying (i) by 3, we get:
⇒ 3x + 3y = 120 ...(iii)
On subtracting (iii) from (ii), we get:
4y = 60
⇒ y = 15
On subtracting y = 15 in (1), we get:
x + 15 = 40
⇒ x = (40 - 15) = 25
Therefore, we have:
$\angle\text{A}=(4\text{x}+20)^\circ=(4\times25+20)^\circ=120^\circ$
$\angle\text{B}=(3\text{x}-5)^\circ=(3\times25-5)^\circ=70^\circ$
$\angle\text{C}=(4\text{y})^\circ=(4\times15)^\circ=60^\circ$
$\angle\text{D}=(7\text{y}+5)^\circ=(7\times15+5)^\circ=(105+5)^\circ=110^\circ$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Linear Equations In Two Variables→Linear Equations In Two Variables — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

Find a fraction which becomes $\Big(\frac{1}{2}\Big)$ when 1 is subtracted from the numerator and 2 is added to the denominator, and the fraction becomes $\Big(\frac{1}{3}\Big)$ when 7 is subtracted from the numerator and 2 is subtracted from the denominator.
→
Given that $\sqrt{2}$ is a zero of the cubic polynomial $6\text{x}^3+\sqrt{2}\text{x}^2-10\text{x}-4\sqrt{2}$ findits other two zeroes.
→
Find the area of a right-angled triangle, the radius of whose circumcircle measure 8cm and the altitude drawn to the hypotenuse measures 6cm.
→
In a right $\triangle\text{ABC},$ right-angled at B, if $\tan\text{A}=1$ then verify that $2\sin\text{A}\cdot\cos\text{A}=1.$
→
Short-Answer Question:
If $\alpha$ and $\beta$ are the zeroes of a polynomial $f(x) = 5x^2 - 7x + 1$, find the value of $\Big(\frac{1}{\alpha}+\frac{1}{\beta}\Big).$
→
A train covers a distance of 300km at a uniform speed. If the speed of the train is increased by 5 km/hr, it take 2 hours less in the journey. Find the original speed of the train.
→
A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is $60^{\circ}$ and from the same point the angle of elevation of the top of the pedestal is $45^{\circ}$. Find the height of the pedestal.
→
Show that (x + 2) is a factor of $f(x) = x^3 + 4x^2 + x - 6.$
→
Write the steps of construction for drawing a pair of tangents to a circle of radius 3cm, which are inclined to each other at an angle of 60º.
→
Draw a right triangle in which sides (other than hypotenuse) are of lengths 4cm and 3cm. Then, construct another triangle whose sides are $\frac53\text{times}$ the corresponding sides of the given triangle.
→