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SATs practice · Year 6Chapter 5 · Geometry: angles and shapes
Year 6 Maths reasoning (SATs) · Geometry: angles and shapes · Lesson 5.2

Year 6 Maths reasoning (SATs): Angles in triangles

Part of the Year 6 Maths reasoning (SATs) geometry: angles and shapes chapter. Chapter overview · whole chapter on one page

5.2

Angles in triangles

Year 6
Calculate unknown angles in a triangle (Year 5-6), Use the properties of isosceles and equilateral triangles (Year 5-6)
Story. Mrs Patel is cutting a triangular piece of fabric for a banner. She knows two of the angles and needs the third, so the corners fit together.

Rule

The angles in a triangle add up to 180 degrees.

In an isosceles triangle, two sides and two angles are equal. In an equilateral triangle, all three angles are 60 degrees.

Key ideas

  • Angles in a triangle: 180 degrees in total.
  • Isosceles: the two base angles are equal.
  • Equilateral: each angle is 60 degrees.
Worked example 5.2.1
In a triangle, two angles are 50 degrees and 70 degrees. Find the third angle, which is angle c.

Method. Take the sum of the two known angles from 180.

  1. Angles in a triangle add up to 180 degrees. Every triangle has three angles that total 180.
    180
  2. Add the two known angles. Add the angles you know.
    50 + 70 = 120
  3. Take the total from 180. Angle c is what is left.
    180 - 120 = 60
  4. Write the answer.
    60

Check. 50 + 70 + 60 = 180. ✓

Watch out. Check that the three angles add up to 180.

50°60°70°
A triangle with angles 50, 60 and 70 degrees (not to the exact scale of the question).
Worked example 5.2.2
An isosceles triangle has an apex angle of 40 degrees. What is each base angle, in degrees?

Method. Take the apex from 180, then share the rest equally between the two base angles.

  1. The two base angles are equal. In an isosceles triangle the base angles are the same.
    base angles are equal
  2. Find the total of the two base angles. Take the apex angle from 180.
    180 - 40 = 140
  3. Share it between the two base angles. Divide by 2.
    140 / 2 = 70
  4. Write the answer.
    70

Check. 40 + 2 x 70 = 180. ✓

Watch out. The two base angles are equal, not the apex and a base angle.

Worked example 5.2.3
A triangle has angles 30 degrees, 30 degrees and x degrees. Find x.

Method. Angles in a triangle add up to 180 degrees.

  1. Add the two known angles. 30 + 30 = 60.
    60
  2. Take from 180. 180 - 60 = 120 degrees.
    120
  3. Write the answer.
    120

Check. 30 + 30 + 120 = 180. ✓

Watch out

Watch out. In a triangle the angles add up to 180 degrees, not 360. Only a quadrilateral has 360 degrees.

Exam tip

Practice guide. Label the equal sides or angles first, so you can see which angles are the same.

Exercise 5B  Practice: angles in triangles

Non-calculator
1
FIn a triangle, two angles are 35 degrees and 85 degrees. Find the third angle, which is angle x.
2
FIn a triangle, two angles are 90 degrees and 28 degrees. Find the third angle, which is angle y.
3
FIn a triangle, two angles are 60 degrees and 60 degrees. Find the third angle, which is angle z.
4
FAn isosceles triangle has an apex angle of 30 degrees. What is each base angle, in degrees?
5
FAn isosceles triangle has an apex angle of 100 degrees. What is each base angle, in degrees?
6
FAn isosceles triangle has an apex angle of 50 degrees. What is each base angle, in degrees?
7
FEach angle of an equilateral triangle is the same size. What is each angle, in degrees?
8
PSA right-angled triangle has one angle of 38 degrees. What is the third angle, in degrees?
9
PSThe angles of a triangle are in the ratio 1:2:3. What is the largest angle, in degrees?
10
RCan a triangle have two obtuse angles? Explain.
11
RBen says a triangle can have angles of 60, 60 and 70 degrees. Is he right? Choose one: Yes, the angles add up to 190 degrees, No, the angles add up to 190 degrees or No, the angles add up to 180 degrees.
12
PSAn isosceles triangle has a top angle of 84 degrees. What is each of the two equal angles, in degrees?
13
FIn triangle ABC, angle A is 50 degrees and angle B is 60 degrees. What is angle C, in degrees?
50°60°70°
14
RProve that the two base angles of an isosceles triangle are equal, if the apex is 40 degrees. Give the reason.

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