Calculating Angles
Triangles
Mixed Bag
100

What is size of x? Give reasons for how you know.


x = 71° (both angles make a right-angle which is equal to 90° OR the angles are complementary).

100

Find the size of angle c. Show your working.

c = 180°- 40° - 60° (angles in a triangle add up to 180°)

c= 60° 

100

Find the size of angle a. Give reasons for how you know.

a = 360° - 110° - 85° - 88° (angles in a quad add up to 360°)

a = 77°

200

What is the size of angle x? Give reasons for how you know.

x = 180° - 49° - 78 ° (angles on str. line add up to 180°)

x = 53°

200

Give name of this triangle according to its angles and sides.

Obtuse scalene triangle

200

Calculate the size of angle x. Give reasons for how you know.


x = (180 ° - 24°)/2

Angles in a triangle add up to 180° and since the triangle is isosceles the base angles are equal.

x = 156/2=78°

300

What is the size of angle e? Give reasons for how you know.


e = 360° - 90° - 127° (angles around a point add up to 360°)

e = 143°

300

What is the value of e? Give reasons for how you know.

The missing angle in the triangle = 180° - 80° - 40° (angles in a triangle add up to 180°)

Missing angle = 60°

e = 180° -60° (angles on a str. line add up to 180°)

e = 120°

300

Find the size of angle c.

The angle opposite 140° is also 140° because opposite angles in a parallelogram are equal. 

So then both of those angles are 140° + 140° = 280°

c = (360° - 280°)/2=40°

(angles inside a quad add up to 360°) 

400

What is beta equal to? Give reasons for your answer.

beta = (180°- 90°) /2

 (angles on a str. line add up to 180°)

(90°)/2=45°

400

What is the value of b?

180° - 135° = 45° (angles on a str. line add up to 180°)

b = 180° - 112° - 45° = 23° (angles in a triangle add up to 180°)

400

141° + 93° = 234° but angles on a straight line add up to 180°

So 234° - 180° = 54° which is the size of the overlap between the green and blue arc

x = 54° (vertically opposite angles are equal)

500

What is y equal to? Give reasons for your answer.


y = 180° - 115° (angles on a str. line add up to 180°)

y = 65°

The other y also equals 65° because vertically opposite angles are equal.

500

Find the angles for all the letters.

d = 57°

e = 57°

f = 66°

500

A quadrilateral has angles of 70°, 34° and two other unknown angles. One of the unknown angles is 55° bigger than the other one. 

What is the value of the unknown angles?

360° - 70° - 34° = 256°

Both unknown angles add up to 256°

(256°)/2= 128°

256° - 55° = 201°

(201°)/2=100,5°

100,5° + 55° = 155,5°

The bigger unknown angle is 155,5° and the smaller unknown angle is 100,5°.

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