A star-patterned quilt has a star with the angles shown. What is the value of x? The diagram is not to scale.

Solution:

In the star pattern drawn below one can see that the angle 105° is an external opposite angle of the two internal angles of the topmost triangle within the pattern.

The relevant formula that needs to be used here is based on the exterior angle theorem. According to the theorem, the external angle is equal to the sum of the opposite interior angles.

The external opposite angle of a triangle = Sum of internal opposite angles

The external angle here in the above diagram is 105° i.e. ∠DCA and the internal opposite angles to it are X° i.e.∠CBA and ∠CAB i.e. 24°.

Therefore we cannot write:

105° = X° + 24°

Hence X° = 105° - 24° = 81°

A star-patterned quilt has a star with the angles shown. What is the value of x? The diagram is not to scale.

Summary:

In the star-patterned quilt, the value of angle x is 81°.