How to Work Out The Missing Angles in an Isosceles Triangle.

An isosceles triangle is triangle with 2 equal side lengths and 2 equal angles. If you are trying to work out the size of the 2 equal angles follow these steps:

Step 1 Take the angle that you are given away from 180⁰ because angles in a triangle add up to 180⁰.

Step 2 All you need to do now is halve this answer.

Let’s take a look at some angle problems in isosceles triangles.

Example A

Work out the size of angles x and y in this isosceles triangle.

Step 1 Take the angle that you are given away from 180⁰ because angles in a triangle add up to 180⁰.

180 – 54 = 126⁰

Step 2 All you need to do now is halve this answer.

½ of 126 is 63⁰. So angles x and y are both 63⁰.

You can check your answer by seeing if the 3 angles add up to 180⁰

63 + 63 + 54 = 180⁰ (as required)

Example B

Work out the size of angles m and n in this isosceles triangle.

Step 1 Take the angle that you are given away from 180⁰ because angles in a triangle add up to 180⁰.

180 – 26 = 154⁰

Step 2 All you need to do now is halve this answer.

½ of 154 is 77⁰. So angles m and n are both 77⁰.

You can check your answer by seeing if the 3 angles add up to 180⁰

77 + 77 + 26 = 180⁰ (as required)

Example C

Work out the size of the 3 angles in a right angled isosceles triangle.

First of all one, of the angles is worth 90⁰ as you are told in the question that the triangle contains a right angle.

Next take this angle way from 180⁰ which leaves you with 90⁰.

Now halve this answer to get 45⁰.

So the 3 angles in an isosceles right angled triangle are 45, 45 and 90.

For some easier question on working out missing angles in other triangles then click here.

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