A straight line has one angle of 110 degrees on one side. Write down the angle on the other side of the straight line.
(1)
2
At a point, three angles are 120 degrees, 90 degrees and x degrees. Work out x.
(1)
3
Two straight lines cross. One angle is 37 degrees. State the vertically opposite angle.
(1)
4
In triangle ABC, angle A = 50 degrees and angle B = 60 degrees. Work out angle C.
(2)
5
On a straight line two adjacent angles are 2x degrees and 40 degrees. These two angles form the straight line. Solve for x.
(2)
6
The angles in a triangle are x degrees, x + 20 degrees and 40 degrees. Find x.
(2)
7
Two straight lines cross. One angle is 2x degrees. The angle vertically opposite to it is 50 degrees. Work out x.
(2)
8
At a point three adjacent angles are 3x degrees, x + 40 degrees and 2x + 20 degrees. Find x.
(3)
9
The three interior angles of a triangle are x degrees, 2x degrees and 3x degrees. Find x.
(2)
10
An exterior angle of a triangle is 110 degrees. This exterior angle equals the sum of the two opposite interior angles. One of the opposite interior angles is 30 degrees. Find the other opposite interior angle.
(2)
11
On a straight line three adjacent angles are x degrees, x + 20 degrees and 2x degrees. The three add to 180 degrees. Find x.
(2)
12
In triangle PQR the angles are (x + 10) degrees, (2x - 20) degrees and 40 degrees. Work out x and then find the angle (2x - 20) degrees.
(3)
13
Two straight lines cross and one small angle is 15 degrees. State the size of the adjacent angle that shares the straight line with the 15 degree angle.
(1)
14
A triangle has angles 40 degrees and 80 degrees. The third angle is split by a line from the opposite vertex into two angles which are equal. Find the size of each of the two equal angles.
(3)
15
At a point a straight line and another line form four angles. Two adjacent angles are 70 degrees and 3x degrees and together they make a straight line. Find x.
(2)
16
A triangle has angles (2x) degrees, (3x - 10) degrees and (x + 20) degrees. Work out x.
(3)
17
Stretch question. A large triangle has angles 50 degrees and 60 degrees. On the side between these angles a smaller triangle is attached sharing that side so that the two triangles together form a quadrilateral. The angle at the shared vertex in the smaller triangle next to the 60 degree angle is 40 degrees and the angle at the shared vertex next to the 50 degree angle is 20 degrees. Find the remaining interior angle of the smaller triangle.
(4)
18
Stretch question. A point has four angles around it made by two crossing lines. The four angles are a, b, c and d in order. Given that a = 2b, and that opposite angles are equal, find b and d.
(4)
Mark scheme · KS3.M-G4 Angles: Lines, Points and Triangles
Question 1
B1 70 degrees cao
Answer: 70 degrees
Question 2
B1 x = 150 degrees cao
Answer: 150 degrees
Question 3
B1 37 degrees cao
Answer: 37 degrees
Question 4
M1 uses sum of angles in a triangle = 180 oe
A1 angle C = 70 degrees cao
Answer: 70 degrees
Question 5
M1 sets up equation 2x + 40 = 180 or equivalent method
A1 x = 70 cao
Answer: 70
Question 6
M1 forms equation x + x+20 + 40 = 180 or equivalent
A1 x = 60 cao
Answer: 60
Question 7
M1 uses vertically opposite angles equal so 2x = 50
A1 x = 25 cao
Answer: 25
Question 8
M1 forms equation 3x + (x+40) + (2x+20) = 360 or equivalent
M1 correctly simplifies to 6x + 60 = 360 and obtains 6x = 300
A1 x = 50 cao
Answer: 50
Question 9
M1 uses x + 2x + 3x = 180 to form 6x = 180
A1 x = 30 cao
Answer: 30
Question 10
M1 uses exterior angle = sum of two opposite interior angles: missing = 110 - 30
A1 80 degrees cao
Answer: 80 degrees
Question 11
M1 forms equation x + (x+20) + 2x = 180
A1 x = 40 cao
Answer: 40
Question 12
M1 forms equation (x+10) + (2x-20) + 40 = 180
M1 solves to give x = 50 (shows 3x + 30 = 180, 3x = 150)
A1 2x - 20 = 80 degrees cao
Answer: 2x - 20 = 80 degrees
Question 13
B1 165 degrees cao
Answer: 165 degrees
Question 14
M1 finds third angle by 180 - (40 + 80) = 60 or equivalent
M1 recognises third angle is split into two equal parts so divides by 2
A1 each angle = 30 degrees cao
Answer: 30 degrees
Question 15
M1 sets up 70 + 3x = 180 or equivalent
A1 x = 36.666... so x = 36 2/3 or x = 110/3 degrees cao
Answer: 110/3
Question 16
M1 forms equation 2x + (3x-10) + (x+20) = 180 or equivalent
M1 simplifies to 6x + 10 = 180 and finds 6x = 170
A1 x = 170/6 = 85/3 cao
Answer: 85/3
Question 17
M1 recognises angles around the shared side add and uses triangle sum for large triangle to find third angle = 70
M1 uses fact that quadrilateral interior angles sum to 360 or alternative method to relate angles
M1 forms equation for smaller triangle angles: unknown + 40 + 20 = 180 or uses subtraction from 360 with other angles
A1 remaining angle = 120 degrees cao
Answer: 120 degrees
Question 18
M1 uses opposite angles equal to get a = c and b = d
M1 uses angles on a straight line (a linear pair) to get a + b = 180
M1 substitutes a = 2b to solve 2b + b = 180 to get b = 60