ANGLES AROUND A POINT WORKSHEET

Find the unknown of the following :

Problem 1 :

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Problem 2 :

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Problem 3 :

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Problem 4 :

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Problem 5 :

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Problem 6 :

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Problem 7 :

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Problem 8 :

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Problem 9 :

Tell whether the statement is always, sometimes, or never true. Explain your reasoning.

a) Complementary angles are adjacent.

b) Angles in a linear pair are supplements of each other.

c) Vertical angles are adjacent.

d)  Vertical angles are supplements of each other.

e) If an angle is acute, then its complement is greater than its supplement.

f)  If two complementary angles are congruent, then the measure of each angle is 45°.

g) Explain why the supplement of an acute angle must be obtuse.

h) Explain why an obtuse angle does not have a complement.

Solution

Problem 10 :

When viewed from the side, the frame of a ball-return net forms a pair of supplementary angles with the ground. Find m∠BCE and m∠ECD

Solution

Problem 1 :

Angles G and H are complementary. If m∠G = 3x + 6 and m∠H = 2x - 11. what is the measure of each angle?

Solution

Problem 2 :

The measures of angles A and B are supplementary. What is the measure of each angle?

Solution

Problem 3 :

An angle is five its supplement. Find both angles.

Solution

Problem 4 :

An angle is 74 degrees more than its complement. Find both angles.

Solution

Problem 5 :

The supplement of an angle exceeds the angle by 60 degrees. Find both angles.

Solution

Problem 6 :

Find the number of degrees in an angle which is 42 less than its complement.

Solution

Problem 7 :

Find the number of degrees in an angle which is 120 less than its supplement. 

Solution

Problem 8 :

The complement of an angle is 30 less than twice the angle. Find the larger angle.

Solution

Problem 9 :

Angles A and B are complementary. If m∠A = 3x - 8 and m∠B = 5x + 10, what is the measure of each angle?

Solution

Problem 10 :

Angles Q and R are supplementary. If m∠Q = 4x + 9 and m∠R = 8x + 3, what is the measure of each angle?

Solution

Problem 1 :

Angles A and B are complementary. If m∠A = 3x - 8 and m∠B = 5x + 10, what is the measure of each angle ?

Solution

Problem 2 :

Angles Q and R are supplementary. If m∠Q = 4x + 9 and m∠R = 8x + 3, what is the measure of each angle ?

Solution

Problem 3 :

Find the measure of two complementary angles ∠A and ∠B, if m∠A = 7x + 4 and m∠B = 4x+ 9.

Solution

Problem 4 :

The measure of an angle is 44 more than the measure of its supplement. Find the measures of the angles.

Solution

Problem 5 :

What are the measures of two complementary angles if the difference in the measures of the two angles is 12.

Solution

Problem 6 :

Find the measures of two supplementary angles ∠N and ∠M if the measure of angle N is 5 less than 4 times the measure of angle M.

Solution

Problem 7 :

Suppose ∠T and ∠U are complementary angles. Find x, if ∠T = 16x - 9 and ∠U = 4x - 1.

Solution

Problem 8 :

Two angles are vertical in relation. One angle is 2y and the other angle is y + 130. Find each angle measure.

Solution

Problem 9 :

The measure of two supplementary angles are in the ratio 4 : 2, Find those two angles.

Solution

Find the value of x in each supplementary angle pair.

Problem 1 :

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Problem 2 :

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Problem 3 :

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Problem 4 :

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Problem 5 :

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Problem 6 :

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Problem 7 :

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Problem 8 :

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Problem 9 :

Two angles form a linear pair. The measure of one angle is five times the measure of the other angle. Find the measure of each angle.

Solution

Problem 10 :

Find the measure of each angle, ∠EFG and ∠LMN are supplementary angles, m∠EFG = (3x + 17)°, and m∠LMN = ((1/2) x − 5)°

Solution

Problem 11 :

Find the angle measure if ∠5 is a supplement of ∠6, and m∠5 = 78°. Find m∠6.

Solution

Problem 12 :

Find the angle measure if ∠7 is a supplement of ∠8, and m∠7 = 109°. Find m∠8.

Solution

Problem 13 :

Find the measure of each angle.

Solution

Problem 14 :

The arm of a crossing gate moves 42° from a vertical position. How many more degrees does the arm have to move so that it is horizontal?

a) 42°      b) 138°      c)  48°        d) 90°

Solution

Problem 15 :

The measure of one angle is 3° more than 1/2 the measure of its supplement.

Solution

Problem 16 :

Two angles form a linear pair. The measure of one angle is 15° less than 2/3 the measure of the other angle.

Solution