Quadrilateral abcd is inscribed in this circle.

what is the measure of angle c?

Step-by-step explanation:

We know that sum of the opposite angles of the quadrilateral inscribed in the circle is 180.

Thus, ∠B+∠D=180°

⇒

⇒

⇒

⇒

Now, substituting the value of x in ∠A, we have

∠A=

Again, sum of opposite angles of the quadrilateral inscribe in circle=180, thus

∠C+∠D=180°

⇒

⇒

Therefore, the measure of ∠C is 107°.

eve and marks ratios are equivalent

step-by-step explanation:

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm