Question

Stonehenge is a circular arrangement of massive stones near Salisbury, England. A viewer at V observes the monument from a point where two of the stones A and B are aligned with stones at the endpoints of a diameter of the circular shape. Given that arc mAB = 48°, what is angle mAVB?

Answer 1

We are given the following measures:

mAB = 48°

mDC = 180°

 

In the given figure above, we can say that angle AVB is an exterior angle which intercepts two arcs, arc AB and arc DC, therefore in this case to solve for the measure of angle mAVB, we have to make use of the formula which is in words:

Find the difference between the measures of the two intercepted arcs and divide by 2, or expressed mathematically in this case as:

mAVB = (mDC – mAB) / 2

 

Substituting the given values into the equation:

mAVB = (180° - 48°) / 2

mAVB = 66°

Answer 2

Angle AVB = 1/2 AB
Angle AVB = 1/2 45 degrees
Angle AVB = 90