Download App

Linear Equation In Two Variable — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsLinear Equation In Two Variable5 Marks
Question
In a cyclic quadrilateral ABCD, it is given that $\angle\text{A}=(\text{2x}+4)^\circ,\ \angle\text{B}=(\text{y}+3)^\circ,$ $\angle\text{C}=(\text{2y}+10)^\circ$ and $\angle\text{D}=(\text{4x}-5)^\circ$ Find the four angles.
✓

Answer

Given that in a cyclic quadrilateral ABCD,
$\angle\text{A}=(\text{2x}+4)^\circ,\ \angle\text{B}=(\text{y}+3)^\circ,$ $\angle\text{C}=(\text{2y}+10)^\circ$ and $\angle\text{D}=(\text{4x}-5)^\circ$
We know that,
Opposite angles of a quadrilateral sum upto 180°
$\Rightarrow\angle\text{B}+\angle\text{D}=180^\circ$
⇒ (y + 3)° + (4x - 5)° = 180°
⇒ 4x + y = 182 ...(i)
Similarly, $\angle\text{A}+\angle\text{C}=180^\circ$
⇒ (2x + 4)° + (2y + 10)° = 180°
⇒ 2x + 2y = 166
⇒ x + y = 83 ...(i)
Subtracting (ii) from (i), we get
⇒ 3x = 99
⇒ x = 33
Substituting x = 33 in (ii), we get
⇒ y = 50
Hence, the angles of ABCD are
So, $\angle\text{A}=70^\circ,\ \angle\text{B}=53^\circ,$ $\angle\text{C}=110^\circ$ and $\angle\text{D}=127^\circ$

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 Question" from Linear Equation In Two Variable→Linear Equation In Two Variable — all question types→Maths STD 10 question papers→Maharashtra Board STD 10 question papers→Maharashtra Board question paper generator→

Similar questions

Solve for x and y:$\frac{5}{\text{x}+\text{y}}-\frac{2}{\text{x}-\text{y}}=-1,$
$\frac{15}{\text{x}+\text{y}}+\frac{7}{\text{x}-\text{y}}=10$
→
The $n^{th}$ term of an AP is $(7 - 4n).$ Find its common difference.
→
Find all the zeros of $(x^4+x^3-23 x^2-3 x+60)$, if it is given that two of its zeros are $\sqrt3$ and $-\sqrt3.$
→
If the point $P(2, 2)$ is equidistant from the points $A(-2, k)$ and $B(-2k , -3)$,
find k. Also, find the length of AP.
→
Solve for x and y:
$\frac{3}{\text{x}}-\frac{1}{\text{y}}+\text{9}=0,$
$\frac{2}{\text{x}}+\frac{3}{\text{y}}=\text{5}$ $(\text{x}\neq0,\ \text{y}\neq0).$
→
Short-Answer Question:
If the zeroes of a polynomial $f(x) = x^3 - 3x^2+ x + 1$ are $(a - b), a$ and $(a + b),$ find a and $b.$
→
Solve for x and y:
$2\text{x}-\frac{3}{\text{y}}=\text{9},$
$\text{3x}+\frac{7}{\text{y}}=\text{2}$ $(\text{y}\neq0).$
→
If $a_n$​​​​​​​ denotes the $n^{th}​​​​​​​$​​​​​​​ term of the AP $2, 7, 12, 17, ....,$ find the value of $(a_{30} - a_{20})$.
→
Solve the following system of equations graphically:
3x + 2y = 12,
5x - 2y = 4
→
​The weights of tea in 70 packets are shown in the following table:
Weight (in grams)
200-201
201-202
202-203
203-204
204-05
205-206
Number of packets
13
27
18
10
1
1
Find the mean weight of packets using step-deviation method.
→