Angle relationships

Find angles in polygons and solve complex parallel line problems.

Space · MA4-ANG-C-01

Sub-topics

Angles in polygons

S = (n - 2) \times 180°

to find unknown angles in polygons and solve algebraic angle problems.

Parallel lines and transversals

Find unknown angles in diagrams involving parallel lines and transversals using corresponding, alternate and co-interior angle properties.

Open Math

Angle relationships

Space · MA4-ANG-C-01

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Date:

Angles in polygons

Q1Straightforward

Find the sum of interior angles of a hexagon.

Q2Straightforward

Find the sum of interior angles of a pentagon.

Q3Straightforward

Find the sum of interior angles of an octagon.

Q4Straightforward

What is the sum of interior angles of a quadrilateral?

Q5Moderate

A pentagon has interior angles of

100°

110°

95°

120°

and

x°

. Find

x

Q6Moderate

Find the size of each interior angle of a regular hexagon.

Q7Moderate

A quadrilateral has interior angles of

72°

95°

113°

and

x°

. Find

x

Q8Moderate

Find the size of each interior angle of a regular octagon.

Q9Challenging

Find the size of each exterior angle of a regular hexagon.

Q10Challenging

The interior angles of a triangle are

x°

2x°

and

3x°

. Find

x

Q11Challenging

Find the size of each exterior angle of a regular pentagon.

Q12Challenging

The interior angles of a quadrilateral are

x°

(x + 20)°

(2x - 10)°

and

(x + 30)°

. Find

x

Parallel lines and transversals

Q13Straightforward

Two parallel lines are cut by a transversal. One of the angles formed at the first intersection is

65°

. Find the size of the corresponding angle at the second intersection.

Q14Straightforward

Two parallel lines are cut by a transversal. An interior angle at one intersection measures

48°

. Find the size of the alternate interior angle at the other intersection.

Q15Straightforward

Two parallel lines are cut by a transversal. One co-interior angle measures

112°

. Find the other co-interior angle.

Q16Straightforward

Two parallel lines are cut by a transversal. One co-interior angle measures

153°

. Find the other co-interior angle.

Q17Moderate

Two parallel lines are cut by a transversal. At the first intersection, angles

a°

and

134°

lie on a straight line. Angle

b°

at the second intersection corresponds to angle

a°

. Find

b

Q18Moderate

Two parallel lines are cut by a transversal. At the upper intersection, angle

x°

and

118°

lie on a straight line. Angle

y°

at the lower intersection is the alternate interior angle to

x°

. Find

y

Q19Moderate

Two parallel lines are cut by a transversal. Angle

p°

is vertically opposite to a

73°

angle at the upper intersection. Angle

q°

at the lower intersection is co-interior to

p°

. Find

q

Q20Moderate

Two parallel lines are cut by a transversal. Angle

m°

at the lower intersection corresponds to a

96°

angle at the upper intersection. Angle

n°

is supplementary to

m°

. Find

n

Q21Challenging

Two parallel lines are cut by a transversal. The co-interior angles are

(3x + 20)°

and

(2x + 40)°

. Find the value of

x

Q22Challenging

Two parallel lines are cut by a transversal. The co-interior angles are

(4x - 15)°

and

(2x + 33)°

. Find the value of

x

Q23Challenging

Two parallel lines are cut by a transversal. The alternate interior angles are

(5x - 10)°

and

(3x + 14)°

. Find the value of

x

Q24Challenging

Two parallel lines are cut by a transversal. The corresponding angles are

(6x - 5)°

and

(4x + 13)°

. Find the value of

x

Worked solutions and answers at openmath.au/year-8/angle-relationships