Angle between Two Lines

Q. In the following figure, two straight lines AB and CD are intersecting each other at the point O. The value of ∠x – ∠y is _____.

1. 62°
2. 118°
3. 56°
4. 180°

Q. Observe the given figure and find the value of unknown angles x and y.

1. x = 112°, y = 40°
2. x = 72°, y = 40°
3. x = 72°, y = 22°
4. x = 112°, y = 22°

Q.

(a) From the given figure find the value of 'x'. [4 MARKS]



(b) In the figure below, x = ${30}^{\circ }$. The value of (6y – 3x) is ___.

Q. Solve : $3x^2$ - $6x$ + $2$ = $0$

Q.

A straight line L through the point (3, -2) is inclined at an angle ${60}^{\circ }$ to the line $\sqrt{3}x+y=1$. If L also intersects the X-axis, then the equation of L is

1. $y+\sqrt{3}x+2-3\sqrt{3}=0$

2. $y-\sqrt{3}x+2+3\sqrt{3}=0$

3. $\sqrt{3}y-x+3+2\sqrt{3}=0$

4. $\sqrt{3}y+x-3+2\sqrt{3}=0$

Q. Equation of a straight line passing through the origin and making an acute angle with $x-$axis twice the size of the angle made by the line $y=\left(0.2\right)x$ with the $x-$axis, is:

1. $y=\left(0.4\right)x$
2. $y=\left(5/12\right)x$
3. $6y-5x=0$
4. $6y+5x=0$

Q. A straight line $L$ through the point $(3,-2)$ is inclined at angle ${60}^o$ to the line $\sqrt{3}+y=1$. If $L$ also intersects the X-axis, then the equation of $L$ is

1. $y+\sqrt{3}x+2-3\sqrt{3}=0$
2. $y-\sqrt{3}x+2+3\sqrt{3}=0$
3. $\sqrt{3}y-x+3+2\sqrt{3}=0$
4. $\sqrt{3}y+x-3+2\sqrt{3}=0$

Q.

The angle between the lines xy = 0 is

1. 

2. 

3. 

4. 

Q. The equations of two equal sides of an isosceles triangle are 7x – y + 3 = 0 and x + y –3 = 0 and the third side passes through the point (1, -10). The equation of the third side is

1. x – 3y – 31 = 0 but not 3x + y + 7 = 0
2. 3x + y + 7 = 0 but not x – 3y – 31 = 0
3. 3x + y + 7 = 0 or x – 3y – 31 = 0
4. Neither 3x + y + 7 nor x – 3y – 31 = 0

Q.

The equation of the pair of straight lines through origin, each of which makes as angle $\alpha$ with the line y = x, is

1. 

2. 

3. 

4. 

Q. Solve:

Q. Find the acute angle between the pair of lines represented by the following equation.
$x^2-7xy+12y^2=0$.

Q.

Let $PQR$ be a right angled isosceles triangle right angled at $P(2,1)$. If the equation of the line $QR$ is $2x+y=3$, then the equation representing the pair of lines $PQ$ and $PR$ is

1. $3x^2-3y^2+8xy+20x+10y+25=0$

2. $3x^2-3y^2+8xy-20x-10y+25=0$

3. $3x^2-3y^2+8xy+10x+15y+20=0$

4. $3x^2-3y^2-8xy-10x-15y-20=0$

Q. Lines $l$ and $m$ and two circles lie in a plane. If $l$ passes through the centers of the two circles and if $m$ is parallel to $l$, which of the following could NOT be the number of points at which $m$ intersects the circles?

1. $0$
2. $1$
3. $3$
4. $4$
5. $5$

Q. Solve: $\frac{x-2}{x+2}+\frac{x+2}{x-2}=4$