Sarin learns Shapes and Solids in school part 54 (Math Question)

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The blog postings are about the Singapore Math. The readers can learn from the postings on Solving Singapore Primary School Mathematics. The blog presents the Math Concept, the Math Questions with solutions that teaches in Singapore Primary Schools. You or the kids can learn the skills to deal with the Math Modeling, the Math Problem Solving and the Problem Sum from Lower Primary School to Upper Primary School level after reading the blog postings. This posting is an upper primary school math question on Angles and Shapes.

Read the posting on Sarin learns Lines and Angles (Math concept) to understand the concept of lines and angles.

Read the posting on Sarin learns Shapes and Solids in school (Math Concept) to know about shapes.

Challenge yourself with the question before look for the given solution‼!

Upper primary school mathematics question UPQ456

In the figure below, no drawn to scale, C is the centre of the circle. AB is the straight line. CD and EC is the radius of the circle.  DCB = 720 and EA = EC. Find the value of  ECD.

Solution:

CD and EC are radius of the circle,

CD = CE = EA

AEC form a isosceles triangle AEC with EA = EC

EAC =   ECA

DEC is exterior of triangle AEC

DEC =   EAC +   ECA = 2 ×   EAC

EDC form a isosceles triangle ECD with CE = CD

EDC =   DEC = 2 ×   EAC = 2 ×   ECA

ECD = 1800 – 2 ×   EDC = 1800 – 4 ×   ECA

AB is a straight line

ECA +   ECD + 720 = 1800

ECA + 1800 – 4 ×   ECA + 720 = 1800

3 ×   ECA =720

ECA = 240

ECD = 1800 – 4 × 240 = 840