INTERIOR AND EXTERIOR ANGLES OF POLYGONS WORKSHEET

Find the indicated angle measures, x.

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Problem 4 :

An exterior angle and the interior angle of a regular polygon are in the ratio 2:7. Find the number of sides of the polygon.

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Problem 5 :

Find the number of sides of a regular polygon whose each exterior angle measures 60°.

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Find x in :

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Problem 9 :

Can a pentagon have angles that measure 120°, 105°, 65°, 150°, and 95°? Explain.

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Problem 10 :

The sum of the angle measures in a regular polygon is 1260°. What is the number of sides of the polygon?

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Problem 11 :

Describe and correct the error in finding the measure of each angle of a regular 20-gon.

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Problem 12 :

The angles of a regular polygon each measure 165°. How many sides does the polygon have?

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Find the values of the variables :

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Problem 7 :

Two angles of a triangle have equal measures, but the third angle's measure is 36° less than the sum of the other two. Find the measure of each angle of the triangle.

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Problem 8 :

Find the measures of the angles of an isosceles triangle if the measure of the vertex angle is 40 degrees less than the sum of the measures of the base angles.

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Problem 9 :

In a triangle ABC, ∠A = 2x + 7, ∠B = 5x - 15, and ∠C = 6x. What is the value of x and what are the measures of angles A, B, and C?

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Problem 10 :

In a triangle XYZ, ∠X = 37°, ∠Y = 45°, and ∠Z = 3x + 6. What is the value of x and what is the measure of ∠Z?

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Problem 11 :

Find the angle measures of a triangle if the second angle measures 10 degrees less than twice the first, and the third angle measures 25 degrees more than the second.

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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

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Problem 2 :

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

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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

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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

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Problem 5 :

The sum of adjacent angles of a parallelogram is

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

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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

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Problem 7 :

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

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Problem 8 :

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

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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.

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Problem 10 :

The diagram shows regular 5 sided polygon with center O.

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Problem 11 :

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