Lines and Angles quiz

The complement of an angle of 35 degrees is:

The supplement of an angle of 110 degrees is:

Angles of a linear pair add up to:

When two lines intersect, vertically opposite angles are:

If two parallel lines are cut by a transversal, alternate interior angles are:

Interior angles on the same side of a transversal cutting two parallel lines are:

An angle greater than 180 degrees but less than 360 degrees is called:

If one angle of a linear pair is 75 degrees, the other is:

Lines which are parallel to the same line are:

Which pair of angles are equal when a transversal cuts two parallel lines?

Find the angle which is equal to its complement. (2 marks)

Find the angle which is four times its supplement. (2 marks)

Two lines intersect and one of the angles formed is 48 degrees. Find the other three angles. (2 marks)

What is the difference between adjacent angles and a linear pair? (2 marks)

State the converse of the Linear Pair Axiom. (2 marks)

If two angles are supplementary and one is twice the other, find them. (2 marks)

A transversal cuts two parallel lines and one alternate interior angle is 72 degrees. Find the other alternate interior angle and the co-interior angle. (2 marks)

Are two right angles supplementary? Are they complementary? (2 marks)

Explain how you would check whether two lines are parallel using a transversal. (2 marks)

Can two acute angles form a linear pair? Explain. (2 marks)

Two complementary angles are in the ratio 2 : 3. Find them. (3 marks)

Lines PQ and RS intersect at O. If angle POR : angle ROQ = 5 : 7, find all four angles. (3 marks)

In a figure, AB is parallel to CD and a transversal makes angles of (5y - 20) degrees and (3y + 40) degrees as alternate interior angles. Find y and the angles. (3 marks)

Rays OA, OB, OC, OD and OE are drawn from a point O so that they form five adjacent angles that together make a complete angle. If four of the angles are 60, 70, 80 and 90 degrees, find the fifth angle. (3 marks)

The difference between two co-interior angles formed by a transversal cutting two parallel lines is 30 degrees. Find the two angles. (3 marks)

Read the passage and answer the questions. A railway track has two parallel rails. A road crosses the tracks diagonally, making an angle of 58 degrees with one rail. (i) What is the road called in geometric terms? (ii) What angle does the road make with the other rail at the corresponding position? (iii) Find the co-interior angle on the same side of the road. (5 marks)

Read the passage and answer the questions. Two roads cross each other at a junction, making four angles. One of the angles is 3x degrees and the angle opposite to it is (x + 50) degrees. (i) Find x. (ii) Find all four angles at the junction. (iii) Name the theorem used. (5 marks)

Read the passage and answer the questions. A ladder leans against a wall, making an angle of 65 degrees with the floor. The floor and the top of the wall are parallel lines and the ladder acts as a transversal. (i) Find the angle between the ladder and the floor on the other side. (ii) Find the alternate interior angle at the top of the wall. (iii) What is the sum of the two co-interior angles? (5 marks)

Read the passage and answer the questions. A window has horizontal parallel bars. A diagonal decorative strip crosses three bars, making an angle of 40 degrees with the top bar. (i) What angle does it make with the middle bar at the corresponding position? (ii) What angle does it make with the bottom bar as an alternate interior angle? (iii) What property allows you to say the top and bottom bars are parallel? (5 marks)

Read the passage and answer the questions. A pair of scissors is opened so that the blades form an angle of 35 degrees. (i) What is the angle between the handles? (ii) What is the angle between one blade and the opposite handle? (iii) Name the angle relationships used. (5 marks)

Prove that if two lines intersect each other, the vertically opposite angles are equal. Use it to find all angles when one angle is 4x + 10 and its vertically opposite angle is 2x + 50 degrees. (6 marks)

Draw two parallel lines cut by a transversal and prove that the pairs of alternate interior angles are equal, using the corresponding angles axiom. (6 marks)

In a figure, AB is parallel to CD, angle APQ = 50 degrees and angle PRD = 127 degrees, where P lies on AB and Q, R lie on CD. Find angle PQR and angle QPR. (6 marks)

Prove that if a transversal intersects two lines such that the bisectors of a pair of corresponding angles are parallel, then the two lines are parallel. (6 marks)

Draw a figure with AB parallel to CD and a point E between them, joined to B on AB and D on CD. If angle ABE = 50 degrees and angle CDE = 40 degrees, find angle BED, drawing an auxiliary line through E. Explain each step. (6 marks)