**Practice** Problems

Use the theorem above to find the measure of angle formed by the intersection of the tangent that intersects chord AC.

By the theorem, the measure of angle is half of the intercepted arc which is 170°.

Therefore $$ x = \frac{1}{2} \cdot 170 = 85^{\circ} $$

Total measure of circle's circumference = 360°

$$ \frac 3 4 (360^{\circ}) = 270^{\circ} $$

By our theorem, we know that the angle formed by a tangent and a chord must equal half of the intercepted arc so $$x = \frac 1 2 \cdot 270^{\circ} =135^{\circ} $$