The idea in brief. Two sides the same length means two angles the same size, so once the third angle is known those two SHARE what is left of the 180°. That is `(180° − a) ÷ 2`, written as ONE line with its reason, and three equal sides are the same sentence one step further: all three angles equal, 60° each. In the lesson. So the two equal angles are each half of what is left.
Lesson video, with the working
Angles in an isosceles triangle
2 min 14 s
The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.
ABC is a triangle and AB and AC are the same length. Angle BAC is 76°. Find angle ABC.
Angle ABC is 52°.
Ans: 52°
Example 1
DEF is a triangle and DE and DF are the same length. Angle EDF is 96°. Find angle x.
Angle x is 42°.
Ans: 42°
How to solve it
Look for the equal sides. The marks say A B and A C are the same length.
So the two angles opposite those sides are the same size.
The three angles in a triangle add up to 180 degrees. The top angle is 76 degrees.
The other two share what is left: 180 minus 76, all divided by 2.
Angle A B C is 52 degrees. Write the property in the bracket.
Two equal sides, and two equal angles. The three angles in a triangle are 180 degrees together. 96 degrees of that is the top angle. So the two equal angles are each half of what is left.
Practice questions with worked solutions
Question 1 is free to try. The other 6 open in the free trial, each with its full working.
each angle of equilateral MNO = 180° ÷ 3 = 60° (angles of an equilateral triangle)
∠MOP = 180° − 60° = 120° (angles on a straight line NOP)
Answer: 120°
For parents
How do you solve isosceles triangle angle questions in P6?
Inside one triangle, the three angles add up to 180°.
What your child learns here
Inside one triangle, the three angles add up to 180°. This Primary 6 page joins that fact to the properties of isosceles and equilateral triangles and to angles on a straight line when a side is extended.
Use the angle sum of a triangle: the three angles add up to 180°.
Recognise an isosceles triangle from the marks on two equal sides, and know the two angles opposite those sides are equal.
Know that every angle of an equilateral triangle is 60°.
When a side is extended, use angles on a straight line to move between the angle outside and the angle inside the triangle.
Does the answer make sense?
Every angle inside a triangle is less than 180°, and in an isosceles triangle each of the two equal base angles must be less than 90°. When your child extends a side, the angle outside and the inside angle next to it make exactly 180°.
How to practise these questions
The Basic questions train the angle sum of a triangle, equilateral triangles with a side extended, and the two equal angles of an isosceles triangle. Intermediate questions add an exterior angle that must be turned back into an angle inside the triangle. Challenge questions write the angles with a letter, or split a triangle with a line so that a second isosceles triangle appears. If the angles inside one triangle do not settle, read the written step-by-step solution.
Questions parents ask
What is the difference between isosceles and equilateral triangles? An isosceles triangle has two equal sides, and the angles opposite them are equal. An equilateral triangle has three equal sides, and each of its angles is 60°.
Is the angle sum of a triangle taught in P6? The angle sum of a triangle is listed under Geometry in the year before Primary 6. In Primary 6 it is used to find unknown angles in composite figures that include triangles.
Why does my child write brackets around 180 minus the angle? The bracket shows that the subtraction is done first and the whole result is then divided by 2. Writing (180° - 40°) ÷ 2 keeps that order clear on paper.
