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

Answer:

$a=44^{\circ},b=136^{\circ},c=77^{\circ},d=57^{\circ}$.

Step-by-step 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, $a=44^{\circ},b=136^{\circ},c=77^{\circ},d=57^{\circ}$.