Parallel Lines And Transversals - Free MCQ Practice Test with solutions,

line a || line c

If two lines make equal angle with the third line. Then the two lines are parallel to each other.
In this case, line a and lines c makes an angle of 30^o with the line b. Therefore, line a and line c are parallel to each other.

Correct Answer :- c

Explanation : Angle d is corresponding angle to a

so , if a = 150^o

then d is also equal to 150^o

Draw a line AB parallel to MN and PQ
 

X = = 

In a parallelogram opposite angles are equal 

∠1 = ∠3  [Corresponding angle are equal]
∠3 = 85°
∠3 + ∠2 = 180°
85° + ∠2 = 180°
∠2 = 95°

60°+ QSR=180°[co interior angles]

QSR=120°

since EF||QS

RFE=QSR (corresponding angles) 

So,RFE=120°

2 = 4 …(vertically opposite angles),

4 = 6 …(Alternate angles)

(2x + 30) = (x + 2y) …(1)

(x+2y) = (3y +10) …(2)

From (1) and (2)

x= 50, y = 40.

Then 5 = 180^o - 6 = 50^o

let ratio be x
a + b = 180° 
2x  + 3x = 180°
5x = 180°
x = 180°/5
x =36°

h = 180° - a 
h = 180° - 2(36°)
h = 180° -72°
h = 108°

ABCD is a parallelogram and ∠ A = 72°

We know that opposite angles of a parallelogram are equal

∴ ∠A = ∠C and ∠B = ∠D

∴ ∠C = 72°

∠A and ∠B are adjacent angles

i.e., ∠A + ∠B = 180°

⇒ ∠B = 180° – ∠A

⇒∠B = 180° – 72° = 108°

∠B = ∠D =108°

Hence, ∠B = ∠D = 108° and ∠C = 72°

Since l and m are parallel lines, the distance between two parallel lines is always the same at every point.

Here,

• AB is perpendicular to both l and m, so AB is the shortest distance between the two parallel lines.
• CD is also perpendicular to both l and m, so CD is also the shortest distance between the same two parallel lines.

The shortest distance between two parallel lines is constant.

Given:
AB = 4 cm
So, CD = 4 cm

Correct Answer: 4 cm