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Maths I

Angle and line facts

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Right angles, straight angles and full turns

When you are dealing with questions involving shapes it is worthwhile to remember these details:

  • Do not assume that an angle is a right angle unless you know of a reason.
  • Most diagrams given in the exam are not drawn to scale. They are usually just sketches so don't rely on measuring them.

Right angles

A right angle is an angle of 90 ^\circ.

Two lines forming a 90 degree angle, which is labelled as such.

Example 1

Question
A right angle, divided into a 70 degree angle and an angle labelled x degrees.

In this diagram a right angle is split into two other angles x ^\circ and 70 ^\circ.

What is the value of x ^\circ?

Answer

We know that x + 70 = 90

So, x = 20

Straight angles

A straight angle is an angle of 180 ^\circ.

A horizontal line. A line arcs over the centre of it and a label beside the arc says 180 degrees.

Example 2

Question
A horizontal line. An orange line emerges from the centre and the angle underneath it is 50 degrees. The angle remaining on the other side is called y degrees.

In this diagram a straight angle is split into two other angles {y ^\circ} and {50 ^\circ}.

What is the value of {y ^\circ}?

Answer

We know that {y + 50 = 180}

So, {y = 130}

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