Exemplification Work out the size of each angle. Diagrams are not drawn accurately. F 72.5 E O 206

162 D _______ FOE _______ Form and solve an equation and find the value of . Mo and Rosie are discussing how to find the missing angle in the

diagram below. Who do you agree with and why? Mo I think you just need to subtract 35 and 98 from 360 35 ? 98 I think that you need to subtract another 90 Rosie

Four line segments are drawn from a point O. They are OA, OB, OC and OD. A, B, C and D are points drawn clockwise in order around O. Angle AOB is 54. Angle BOC is 106. Angle BOD is 187. What is the size of angle AOD? Circle the correct answer. 13 81 119 347

Calculate the size of the missing angle in each diagram. 38 ? 73 ? 81 Amir and Whitney are discussing a diagram. Angle WXY is 19 Amir

Angle YXZ is 161 Y, X and Z all lie on the same line. XY and XZ are two different lines intersecting at X. Whitney Who do you agree with? You must justify your answer with a sketch. CD and EF are straight lines. Write expressions for the size of any missing angles. Use the correct three letter and geometric notation where appropriate.

G C F O E D Use letter notation to describe the angle that is vertically opposite to

the angle already indicated by an arc. Z J M K Y N C X

L Q R P O U T S V W

Explain why each of these diagrams do not show vertically opposite angles? The following diagram shows three straight lines that intersect at a single point. Work out the value of and . 42 12

Calculate the size of the angle marked in each diagram. 72 43 51 Bella says, Angle can be any angle and is double that. Milo says, Five lots of angle must be equal to 180. Who do you agree with? Why?

A C B Two shapes are connected at their edges as in the diagram below. Calculate the size of the obtuse angle VWX. X

V 35 W Y Z One angle in an isosceles triangle is 30. What are the other two angles? Give two possible solutions. What are the sizes of angles ADC, EFG and LKP.

M D C L 129 72 K B

N 111 F 68 P 85 H A

G E Q 120 50 J R David draws the diagram. He says the interior angles in a quadrilateral sum to 720 because he

has split the shape into four triangles and four lots of 180 is 720 Explain why Davids diagram does not show this. Which of the following equations are correct using the diagram? 81 Fill in the blanks. Y

Angles on a straight line sum to _______. X 61 Therefore angle WXZ is ________. The interior angles in a triangle sum to _______ so the other two angles in the triangle must sum to _______. W

Z Fill in the blanks. A Angle CEB is ______ because __________ __________________________________ _______. C 52 E BED is ______ because _____________ _________________________________

______. D B Write as many equations as possible for the diagram. You must state the angle facts that you have considered to write each equation. a c b

d e f g Find the size of the angle specified for each diagram. D G E 103 51 n

H F n _____ EDF _____ Below is a diagram and a student explanation of finding the size of angle QPS. Is each stage of reasoning correct? Could the solution have been more efficient? TRU 125 because angles on a straight line sum to 180.

P Q QRS TRU 125 because vertically opposite angles are equal. 100 S QPS 75 because angles in a quadrilateral sum to 360.

60 R T 55 U The diagram shows two polygons connected by one of their vertices at a point. Determine if the quadrilateral is a square or not. How do you know? The diagram is not drawn accurately. 108 32

Aliya and Theo are forming polygons by combining pattern blocks. Aliyah puts a square and a triangle together as shown to form polygon 1. Theo puts two squares together as shown to form polygon 2. Aliya Theo The interior angles of a square and triangle sum to 180 and 360 respectively. The interior angles of the pentagon must sum to 540.

The interior angles of polygon 2 must be 720 because the sum of the interior angles in each square is 360. Polygon 1 Polygon 2 Explain whether you agree or disagree with each person. The diagram to the right shows an equilateral triangle, a square and a regular pentagon all sharing the edge AB. Find the size of angles:

D CDE EAH C F H G

FBH B A E A regular polygon has an interior angle of 172. How many edges does the polygon have? Measure all of the angles below. What do you notice? Use dynamic geometry software to see if this is always the case.

Look at the map. All of the odd numbered streets are parallel. All of the even numbered avenues are parallel. Mark on all of the parallel lines with appropriate notation. Mark any angles that you think will be the same. 27th St. 25th St. 10th Av. y

wa rro Na 8th Av. Does it matter whether the transversal lines are perpendicular to the streets? 23rd St. Which of the following statements are true? F

AB is parallel to CD. A Lines through AB and CD will meet exactly once. C CHE FHD G B 72

H D 74 E Find as many pairs of angles as possible that are the same. Find as many pairs of angles as possible that sum to 180. State whether each pair is corresponding, alternate or co-interior.

Find the size of the following angles. You must give reasons for your solution.

How many different ways can you justify your solution? Which justification is the most efficient? X UYZ ______ Z WYV ______ S 152 SZX ______

VYZ ______ XZT ______ U W T V Y Points A, B and C all lie on a straight line. Find the size of angle BAE in the diagram below. Give reasons for your solution.

A B D 52 138 C E Write down as many equations as possible that you know to be true using the diagram below. You must provide reasons for each equation.

Use your equations to prove that the exterior angle of a triangle is equal to the sum of the two opposite interior angles. Prove that angle is equal in size to angle in the diagram below. Explain your reasoning in full.

By considering a convex kite as two different isosceles triangles. Prove that a convex kite has a pair of opposite angles that are equal. Does your proof work for a concave kite? If not, can you find a proof that will work for all kites?