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11+ · Angles

EP.M117 Angles on Lines, at Points and in Triangles

GL ASSESSMENT GL-11PLUS-MATHS · Calculators not allowed · about 55 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

A straight line contains two adjacent angles. One angle measures 65 degrees and the other is x degrees. What is x?

A) 65
B) 115
C) 125
D) 55
E) 180

(Total for Question 1 is 1 mark)

Four angles around a point are 140 degrees, 85 degrees, 45 degrees and x degrees. Calculate x.

A) 75
B) 80
C) 85
D) 90
E) 95

(Total for Question 2 is 1 mark)

In triangle ABC the angles at A and B are 50 degrees and 60 degrees. Work out the angle at C.

A) 60
B) 70
C) 80
D) 90
E) 50

(Total for Question 3 is 1 mark)

The three angles of a triangle are 3x, 2x and x degrees.

Calculate x and find the size of each angle.

(Total for Question 4 is 2 marks)

Triangle PQR is isosceles with PQ = PR. Angle Q measures 48 degrees.

Find angle P.

(Total for Question 5 is 2 marks)

Three adjacent angles on a straight line are 2x, 3x and 4x.

(a)Find x.(2)

(b)Find each angle.(2)

(Total for Question 6 is 4 marks)

In triangle ABC angle B = 40 degrees. The exterior angle at C (formed by extending BC) measures 110 degrees.

Find angle A.

(Total for Question 7 is 2 marks)

An isosceles triangle has its apex angle equal to 36 degrees. What is the size of each base angle?

A) 72
B) 82
C) 54
D) 144
E) 36

(Total for Question 8 is 1 mark)

At vertex B of triangle ABC the exterior angle (outside the triangle) measures 120 degrees. Inside the triangle angle C measures 30 degrees.

Calculate angle A.

(Total for Question 9 is 2 marks)

Triangle ABC has AB = AC. Angle B = 58 degrees.

Give the size of angle C and state a reason for your answer.

(Total for Question 10 is 2 marks)

Five angles around a point are x degrees, 2x degrees, 3x degrees, 40 degrees and 20 degrees.

(a)Find x.(2)

(b)Find each angle in degrees.(2)

(Total for Question 11 is 4 marks)

Give a brief reason why the three interior angles of any triangle add up to 180 degrees.

(Total for Question 12 is 1 mark)

Triangle DEF is isosceles with DE = DF. The base angles are (x + 15) degrees and (2x - 5) degrees.

(a)Find x.(2)

(b)Find the three angles.(1)

(Total for Question 13 is 3 marks)

Triangle ABC is isosceles with AB = AC. The exterior angle at B (outside the triangle) measures 110 degrees.

Find the three interior angles of the triangle.

(Total for Question 14 is 3 marks)

In a right-angled triangle one acute angle is 45 degrees. What is the other acute angle?

A) 35
B) 45
C) 55
D) 90
E) 135

(Total for Question 15 is 1 mark)

Mark scheme · EP.M117 Angles on Lines, at Points and in Triangles

Question 1

B1 correct option B (115) cao
Answer: B) 115 degrees, because 65 + 115 = 180 (straight line). (Answer: 115 degrees.)

Question 2

B1 correct option D (90) cao
Answer: D) 90 degrees (360 - (140 + 85 + 45) = 90).

Question 3

B1 correct option B (70) cao
Answer: B) 70 degrees (180 - 50 - 60 = 70).

Question 4

M1 form correct equation 3x + 2x + x = 180 or 6x = 180 seen
A1 x = 30 and angles 90, 60, 30 cao
Answer: x = 30. The angles are 3x = 90 degrees, 2x = 60 degrees, x = 30 degrees.

Question 5

M1 state that base angles at Q and R are equal (or identify two angles are 48) or set up 48 + 48 + P = 180
A1 P = 84 degrees cao
Answer: 84 degrees (180 - 48 - 48 = 84).

Question 6

(a) M1 form equation 2x + 3x + 4x = 180 or 9x = 180
(a) A1 x = 20 cao
(a) Answer: x = 20
(b) M1 substitute x = 20 into 2x, 3x, 4x seen or equivalent
(b) A1 angles 40, 60 and 80 degrees cao
(b) Answer: 2x = 40, 3x = 60, 4x = 80

Question 7

M1 use exterior angle = sum of opposite interior angles (A + B = exterior) or state A = exterior - B
A1 A = 70 degrees cao
Answer: 70 degrees (A = 110 - 40).

Question 8

B1 correct option A (72) cao
Answer: A) 72 degrees ((180 - 36)/2 = 72).

Question 9

M1 use exterior angle = sum of opposite interior angles so A = exterior - C
A1 A = 90 degrees cao
Answer: 90 degrees (A = 120 - 30).

Question 10

B1 Angle C = 58 degrees cao
B1 reason: angles opposite equal sides are equal (or 'base angles are equal')
Answer: Angle C = 58 degrees. Reason: angles opposite equal sides are equal (base angles equal in an isosceles triangle).

Question 11

(a) M1 form equation x + 2x + 3x + 40 + 20 = 360 or 6x + 60 = 360
(a) A1 x = 50 cao
(a) Answer: x = 50
(b) M1 substitute x = 50 into expressions or list values
(b) A1 angles 50, 100, 150, 40 and 20 degrees cao
(b) Answer: Angles are 50, 100, 150, 40 and 20 degrees.

Question 12

B1 reference to drawing a parallel through a vertex and using alternate interior angles to show sum 180, or statement 'straight line = 180 and alternate interior angles show two angles add to a straight line' oe
Answer: Because if a line is drawn through one vertex parallel to the opposite side the two alternate interior angles plus the vertex angle make a straight line (180 degrees).

Question 13

(a) M1 use equality of base angles: x + 15 = 2x - 5 or equivalent
(a) A1 x = 20 cao
(a) Answer: x = 20
(b) A1 angles 35, 35 and 110 degrees cao
(b) Answer: Base angles are 35 degrees and 35 degrees, vertex angle = 110 degrees.

Question 14

M1 use exterior angle = sum of opposite interior angles and set up equations (let base angle = b, vertex = v and use v + b = 110 and v + 2b = 180 or equivalent)
M1 solve to find b = 70 and v = 40 (or show correct substitution)
A1 angles 40, 70, 70 degrees cao
Answer: Angles are 40 degrees (vertex), 70 degrees and 70 degrees (base angles).

Question 15

B1 correct option B (45) cao
Answer: B) 45 degrees (90 - 45 = 45).

Angles on Lines, at Points and in Triangles - Worksheets, Questions and Revision

EP.M117 Angles on Lines, at Points and in Triangles

Question 1

Question 2

Question 3

Question 4

Question 5

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Question 10

Question 11

Question 12

Question 13

Question 14

Question 15