Answer:
[tex]a=44^{\circ},b=136^{\circ},c=77^{\circ},d=57^{\circ}[/tex].
Step-by-step explanation:
It is given that a and 46° are complementary angles.
[tex]a+46^{\circ}=90^{\circ}[/tex]
[tex]a=90^{\circ}-46^{\circ}[/tex]
[tex]a=44^{\circ}[/tex]
It is given that a and b are supplementary angles.
[tex]a+b=180^{\circ}[/tex]
[tex]44^{\circ}+b=180^{\circ}[/tex]
[tex]b=180^{\circ}-44^{\circ}[/tex]
[tex]b=136^{\circ}[/tex]
Angle conjugate to c is 283°.
[tex]c+283^{\circ}=360^{\circ}[/tex]
[tex]c=360^{\circ}-283^{\circ}[/tex]
[tex]c=77^{\circ}[/tex]
Sum of all angles at a point is 360 degrees.
[tex]a+b+c+d+46^{\circ}=360^{\circ}[/tex]
[tex]44^{\circ}+136^{\circ}+77^{\circ}+d+46^{\circ}=360^{\circ}[/tex]
[tex]d+303^{\circ}=360^{\circ}[/tex]
[tex]d=360^{\circ}-303^{\circ}[/tex]
[tex]d=57^{\circ}[/tex]
Therefore, [tex]a=44^{\circ},b=136^{\circ},c=77^{\circ},d=57^{\circ}[/tex].
