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Geometry - Calculating missing angles on a straight line and at a point

Grade 5IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Angles on a straight line always sum to 180 degrees.

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Angles around a point (a full turn) always sum to 360 degrees.

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A right angle is exactly 90 degrees and is often marked with a small square.

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To find a missing angle, subtract the sum of the known angles from the total (180 or 360).

📐Formulae

Angle a+Angle b=180∘\text{Angle } a + \text{Angle } b = 180^\circ (for two angles on a straight line)

∑Angles on a straight line=180∘\sum \text{Angles on a straight line} = 180^\circ

∑Angles at a point=360∘\sum \text{Angles at a point} = 360^\circ

💡Examples

Problem 1:

A straight line is divided into two angles. One angle is 125∘125^\circ. Find the size of the missing angle xx.

Solution:

x=55∘x = 55^\circ

Explanation:

Since angles on a straight line add up to 180∘180^\circ, we calculate 180∘−125∘=55∘180^\circ - 125^\circ = 55^\circ.

Problem 2:

Four angles meet at a point. Three of the angles are 90∘90^\circ, 110∘110^\circ, and 85∘85^\circ. Calculate the fourth angle yy.

Solution:

y=75∘y = 75^\circ

Explanation:

Angles around a point sum to 360∘360^\circ. First, add the known angles: 90+110+85=285∘90 + 110 + 85 = 285^\circ. Then, subtract from the total: 360∘−285∘=75∘360^\circ - 285^\circ = 75^\circ.

Problem 3:

On a straight line, there are three angles: 40∘40^\circ, a right angle, and an unknown angle zz. Find zz.

Solution:

z=50∘z = 50^\circ

Explanation:

A right angle is 90∘90^\circ. The total for a straight line is 180∘180^\circ. So, z=180∘−(40∘+90∘)=180∘−130∘=50∘z = 180^\circ - (40^\circ + 90^\circ) = 180^\circ - 130^\circ = 50^\circ.