Question

In the figure given at right, find :​

Answer 1

Step-by-step explanation:

Given :-

From the given figure:

angle CBA = 40° and angle CAB = 15°

angle CDE = 52° .

To find :-

Find the values of angle DCE and angle AED

Solution:-

From the given figure :

In ∆ ABC , we have

angle CBA = 40° and angle CAB = 15°

and the side BC is produced to D then an

exterior angle ACD is formed

we know that

An exterior angle is equal to the sum of two

opposite interior angles in a triangle

=>angle ACD = angle CBA+ angle CAB

=>angle ACD = 40°+15°

=>angle ACD = 55°

And ,

In ∆ ECD , we have

angle ECD = 55°

angle CDE = 52°

The side EC is produced to A so that angle AED

is formed

We know that

An exterior angle is equal to the sum of two

opposite interior angles in a triangle

=>angle AED = angle DCE +angle CDE

=>angle AED = 55°+52°

=>angle AED = 107°

Answer:-

The values of the unknown angles are

angle ECD = 55°

angle AED = 107°

Used formula:-

An exterior angle is equal to the sum of two opposite interior angles in a triangle