Question

in the diagram ,a and 46° are complementary angles. It is given that a and b are supplementary angles and the angle conjugate to c is 283°. Calculate the values of a,b,c and d.​ pleaseeeee answer soonn

Answer 1

`a=44^(\circ),b=136^(\circ),c=77^(\circ),d=57^(\circ)`.

Explanation:

It is given that a and 46° are complementary angles.

`a+46^(\circ)=90^(\circ)`

`a=90^(\circ)-46^(\circ)`

`a=44^(\circ)`

It is given that a and b are supplementary angles.

`a+b=180^(\circ)`

`44^(\circ)+b=180^(\circ)`

`b=180^(\circ)-44^(\circ)`

`b=136^(\circ)`

Angle conjugate to c is 283°.

`c+283^(\circ)=360^(\circ)`

`c=360^(\circ)-283^(\circ)`

`c=77^(\circ)`

Sum of all angles at a point is 360 degrees.

`a+b+c+d+46^(\circ)=360^(\circ)`

`44^(\circ)+136^(\circ)+77^(\circ)+d+46^(\circ)=360^(\circ)`

`d+303^(\circ)=360^(\circ)`

`d=360^(\circ)-303^(\circ)`

`d=57^(\circ)`

Therefore,
`a=44^(\circ),b=136^(\circ),c=77^(\circ),d=57^(\circ)`.