Question

5. In the following figure, DE and EC are the bisectors of angleC and angleD. If the sum of angleC and angleD is 180°, then the measure of angle CED​

Answer 1

Ans:-

An(EDC) = An(EDA) [as ED is bisector ]

and

An(ECB) = An(ECD) [as EC is bisector ].

Now An(ADC)+ An(BDC) = 180

SO, An(ADE)+ An(EDC) + An(ECB)+ An(ECD) = 180

Now from above,

replace ADE by EDC and ECD by ECD:-

WE GET:-

2[An(EDC) + An(ECD)] = 180

so, An(EDC) + An(ECD) = 90

.

Now in TRIANGLE ECD

An(EDC) + An(ECD) + An(CED) = 180

[sum of interior angles of triangle is 180]

90 + An(CED) = 180

SO, An(CED) = 90

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