PRACTICE PROBLEMS ON EXTERIOR ANGLE THEOREM

Problem 1 :

Find m∠A and m∠B.

Solution

Problem 2 :

Find ∠M and ∠N

Solution

Problem 3 :

Find ∠D and ∠C

Solution

Problem 4 :

Find ∠L and ∠M

Solution

Problem 5 :

Find m∠ACB, m∠BCD and m∠DCE.

Solution

Problem 6 :

Find m∠K, m∠L, m∠KML, m∠LMN.

Solution

Problem 7 :

Find the measure of the exterior angle. Solve for z.

Solution

Problem 8 :

Find the measures of the exterior angles of each polygon. Solve for x.

Solution

Problem 9 :

Find the measures of the exterior angles of each polygon. Solve for z.

Solution

Problem 10 :

Find the measures of the exterior angles of the polygon.

Problem 11 :

In FGH, m∠F = 42 and an exterior angle at vertex H has a measure of 104. What is m∠G?

a) 34      b) 62     c) 76     d) 146

Solution

Problem 12 :

In the diagram below of ABC, side BC is extended to point D, m∠A = x, m∠B = 2x + 15, and m∠ACD = 5x + 5.

What is m∠B?

a) 5       b) 20     c) 25       d) 55

Solution

Find, giving reasons, the value of x:

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

Solution

Find the values of the variables in the following diagrams:

Problem 5 :

Solution

Problem 6 :

Solution

Problem 7 :

Solution

Problem 8 :

Solution

Problem 9 :

Solution

Problem 10 :

Solution

Problem 11 :

Solution

Problem 12 :

In FGH, m∠F = 42 and an exterior angle at vertex H has a measure of 104. What is m∠G?

1) 34    2) 62      3) 76     4) 146

Solution

Problem 13 :

In the diagram below of ABC, side BC is extended to point D, m∠A = x, m∠B = 2x + 15, and m∠ACD = 5x + 5.interior-angle-of-trianglenq1.png

What is m∠B?

1) 5       2) 20        3) 25      4) 55

Solution

Problem 14 :

In ABC shown below, side AC is extended to point D with m∠DAB = (180 − 3x)°, m∠B = (6x − 40)°, and m∠C = (x + 20)°.

What is m∠BAC?

Solution

Problem 15 :

In the diagram below of ABC, BC is extended to D.

If m∠A = x² − 6x, m∠B = 2x − 3, and m∠ACD = 9x + 27, what is the value of x?

1) 10     2) 2     3) 3     4) 15

Problem 1 :

The number of sides of a regular polygon where each exterior angle has a measure of 45^º is ……

a)  8        b) 10       c) 4     d) 6

Solution

Problem 2 :

a)  60^º      b) 140^º      c) 150^º     d) 108^º

Solution

Problem 3 :

If two adjacent angles of a parallelogram are in the ratio 2 : 3, then the measure of angles are 

(a) 72^º, 108^º     (b) 36^º, 54^º     (c) 80^º, 120^º    (d) 96^º, 144^º

Solution

Problem 4 :

If PQRS is a parallelogram, then ∠P - ∠R is equal to

a) 60^º     b) 90^º    c) 80^º    d) 0^º

Solution

Problem 5 :

The sum of adjacent angles of a parallelogram is

a) 180^º     b) 120^º  c) 360^º  d) 90^º

Solution

Problem 6 :

The number of sides of a regular polygon whose each interior angle is of 135^º is ……

a) 6       b) 7      c) 8        d) 9

Solution

Problem 7 :

The figure given below is a regular pentagon, find the value of x.

Solution

Problem 8 :

A polygon has an interior angle that is five times larger than the exterior angle. How many sides does it have?

Solution

Problem 9 :

The diagram shows three regular pentagons meeting at a point. Work out the size of the angle marked x. You must show all your working.

Solution

Problem 10 :

The diagram shows regular 5 sided polygon with center O.

Shape A is a regular triangle. Shape B is a regular octagon.

Another regular polygon, P, is shown on the diagram.

How many sides does polygon P have? You must show your working.

Solution