What are vertically opposite angles? (or vertical angles). Angles on intersecting lines.
If you have 2 straight lines that intersect at a point, then the angles opposite each other are the same. These type of angles are called vertically opposite angles in the UK or vertical angles in the US.
Work out angles x, y and z. Give reasons for each answer.
Angle x is equal to 43⁰ as angle x is opposite the 43⁰ angle (vertically opposite angles are equal).
Now since the angle around a point add up to 360⁰, then angles y and z can be found by subtracting the two 43⁰ angles from 360⁰ and halving your answer.
360 – 43 – 43 = 274⁰.
And 274⁰ ÷ 2 = 137⁰.
So angles y and z are 137⁰.
You can confirm your angles are correct by seeing if they add up to 360⁰
43 + 43 + 137 + 137 = 360⁰.
A quicker way to find angles y and z is to just take the 43⁰ from 180⁰ (as angles on a straight line add up to 180⁰) So 180 – 43 = 137⁰.
Either way will be acceptable in an exam situation.
The diagram shows two intersecting lines. Calculate angles m and n. Explain your answers.
Angle m is equal to 109⁰ as angle m is opposite the 109⁰ angle (vertically opposite angles are equal).
Like example 1, angle n can be found by subtracting the two 109⁰ angles from 360⁰ and halving your answer.
360 – 109 – 109 = 142⁰.
And 142⁰ ÷ 2 = 72⁰
So angle n is equal to 71⁰.
Again you can check that all the angles add to 360⁰
71 + 71 + 109 + 109 = 360⁰.
Alternatively, you could just take the 109 off 180 to give 71 as angles on a straight line add up to 180.