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Shape, Space and Measure (Intermediate) - Angles in Shapes
 
Angles in a Triangle | Angles in a Quadrilateral
Angles in a Triangle
 
The sum of the angles in a triangle is 180o .
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This property can be used to solve problems on angles.
 
For Example:
1) Given triangle ABC with angle BAC=100o and angle BCA=20o, Calculate angle ABC.
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The method is to add the two angles given and subtract this total from 180.

Note: reasons are often asked for and should be given briefly, in brackets.
 
2) Given triangle LMN with angle LMN=50o and LM= LN, calculate angle LNM, angle MLN and angle LNP.

 

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3) Given triangle PQR with PQR =30o, the line RS is parallel to PQ and PRS=90o. Calculate Angles QPR, QRP and SRT.
 
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Angles in a Quadrilateral

The sum of the angles in a quadrilateral is 360o.
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Again this property can be used to calculate missing angles.
 
For Example:
1) Given the quadrilateral PQRS, calculate Angle PQR.
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2) Given the parallelogram LMNO, with Angle LON = 70o. Calculate Angles OLM, LMN and MNO.
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For angles in Polygons, see under ‘Regular and Irregular Polygons, exterior and interior angles’.