Angle BAC unrolled, BAR = 86 degrees. From point A, ray AS emanates so that RAS = 52 degrees.

Angle BAC unrolled, BAR = 86 degrees. From point A, ray AS emanates so that RAS = 52 degrees. Find the angle CAS. How many solutions does the problem have?

This problem can have two solutions:

when the AS beam lies inside the RAC angle.
when the AS beam lies inside the BAR angle.
Let’s consider the first case.

The angle BAC is expanded, equal to 180 °.

Angle BAC = angle BAR + angle RAS + angle CAS = 180 °.

Angle BAC = 86о, angle RAS = 52о.

86о + 52о + CAS angle = 180о.

Angle CAS = 180 ° – 86 ° – 52 ° = 42 °.

Let’s consider the second case.

Angle BAR = angle BAS + angle SAR = 86 °.

angle SАR = 52о.

angle BAS + 52о = 86о.

Angle BAC = 86о – 52о = 34о.

CAS Angle = BAC Angle – BAC Angle = 180 ° – 34 ° = 146 °.

Answer: CAS angle = 146о or CAS angle = 42о.