I need help!! Find the area of each shaded segment. Round your answer to the nearest 10th

Given:

θ = 60°

Radius = 8 in

To find:

The area of the shaded segment.

Solution:

Vertically opposite angles are congruent.

Angle for the shaded segment = 60°

Area of the sector:

A = 33.5 in²

Area of the sector = 33.5 in²

Area of triangle:

A = 32 in²

Area of the triangle = 32 in²

Area of segment = Area of sector - Area of triangle

                            = 33.5 in² - 32 in²

                            = 1.5 in²

The area of the shaded segment is 1.5 square inches.

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°