A straight line has one angle of 128 degrees on one side. Write down the angle on the other side of the straight line.
(1)
2
At a point, three angles are 95 degrees, 140 degrees and x degrees. Work out x.
(1)
3
Two straight lines cross. One angle is 63 degrees. State the vertically opposite angle.
(1)
4
In triangle ABC, angle A = 35 degrees and angle B = 85 degrees. Work out angle C.
(2)
5
A triangle has one interior angle of 50 degrees and another of 70 degrees. State the exterior angle at the third vertex.
(1)
6
On a straight line, two adjacent angles are 3x degrees and 45 degrees. Find x.
(2)
7
At a point, four angles are formed. Three of them are 90 degrees, 120 degrees and 80 degrees. Find the fourth.
(1)
8
The angles in a triangle are x degrees, x + 10 degrees and 50 degrees. Find x.
(2)
9
Two straight lines cross. One angle is 3x degrees. The angle vertically opposite to it is 57 degrees. Work out x.
(2)
10
At a point three adjacent angles are 4x degrees, 5x degrees and 3x degrees. Find x.
(2)
11
An exterior angle of a triangle is 130 degrees. This exterior angle equals the sum of the two opposite interior angles. One of the opposite interior angles is 55 degrees. Find the other.
(2)
12
The three interior angles of a triangle are x degrees, 3x degrees and 5x degrees. Find x.
(2)
13
On a straight line, three adjacent angles are x degrees, x + 30 degrees and 2x + 10 degrees. Find x.
(2)
14
At a point, three adjacent angles are 4x degrees, 2x + 30 degrees and x + 50 degrees. Find x.
(3)
15
In triangle PQR, angle P = (x + 15) degrees, angle Q = (2x - 5) degrees and angle R = 50 degrees. Work out x and then find angle Q.
(3)
16
A road is straight. A path leaves the road, making an angle of (4x + 10) degrees with the road on one side and (2x + 20) degrees with the road on the other side. Find x.
(3)
17
Two straight lines cross at O. One pair of vertically opposite angles is 4x degrees and (2x + 50) degrees. Find x, and hence find the size of these two angles.
(3)
18
Triangle XYZ is isosceles with XY = XZ. Angle XYZ = (3x - 10) degrees and angle XZY = (x + 30) degrees. Find x and the size of angle YXZ.
(3)
19
Stretch question. A large triangle has angles 55 degrees and 65 degrees. A line from the vertex between these two angles splits the third angle into two parts in the ratio 2:3. Find the size of each of the two parts.
(4)
Mark scheme · KS3.M-G4D Angles: Lines, Points and Triangles: Fluency and Exam Drill
Question 1
B1 52 degrees cao
Answer: 52 degrees
Question 2
B1 x = 125 degrees cao
Answer: 125 degrees
Question 3
B1 63 degrees cao
Answer: 63 degrees
Question 4
M1 uses sum of angles in a triangle = 180 oe
A1 angle C = 60 degrees cao
Answer: 60 degrees
Question 5
B1 120 degrees cao (exterior angle = sum of the two remote interior angles)
Answer: 120 degrees
Question 6
M1 sets up 3x + 45 = 180 or equivalent
A1 x = 45 cao
Answer: 45
Question 7
B1 70 degrees cao
Answer: 70 degrees
Question 8
M1 forms equation x + (x+10) + 50 = 180 or equivalent
A1 x = 60 cao
Answer: 60
Question 9
M1 uses vertically opposite angles equal so 3x = 57
A1 x = 19 cao
Answer: 19
Question 10
M1 forms equation 4x + 5x + 3x = 360
A1 x = 30 cao
Answer: 30
Question 11
M1 uses exterior angle = sum of the two opposite interior angles: missing = 130 - 55
A1 75 degrees cao
Answer: 75 degrees
Question 12
M1 uses x + 3x + 5x = 180 to form 9x = 180
A1 x = 20 cao
Answer: 20
Question 13
M1 forms equation x + (x+30) + (2x+10) = 180
A1 x = 35 cao
Answer: 35
Question 14
M1 forms equation 4x + (2x+30) + (x+50) = 360 or equivalent
M1 simplifies to 7x + 80 = 360 and obtains 7x = 280
A1 x = 40 cao
Answer: 40
Question 15
M1 forms equation (x+15) + (2x-5) + 50 = 180
M1 simplifies to 3x + 60 = 180 and solves x = 40
A1 angle Q = 75 degrees cao
Answer: x = 40, angle Q = 75 degrees
Question 16
M1 sets up (4x+10) + (2x+20) = 180
M1 simplifies to 6x + 30 = 180 and obtains 6x = 150