Question

Determine and state the measure of angle F

Answer 1

∠ F = 94°

Explanation:

The opposite angles of the quadrilateral are supplementary, thus

∠ D + ∠ F = 180°, that is

86° + ∠ F = 180° ( subtract 86° from both sides )

∠ F = 94°

Answer 2

94

Explanation:

Angle <D is an inscribed angle and the measure of it is equal to the half of the arc it sees

so the measure of arc EFG is 2×86° = 172°

Since the perimeter of a circle is 360° the measure of arc EDG would be 360 - 172 = 188

Therefore since the measure of angle <F should be half of the arc it sees as well the answer is 188 ÷ 2 = 94