Use the Exterior Angle Theorem to find the measure of each angle.

∠ C = 36°

∠ D= 81°

∠ DEC= 63°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the interior opposite angles.

∴   (11y + 4) + (5y + 1) = 117

         11y + 4 + 5y + 1 = 117

         16y + 5 = 117

         16y = 117-5

         16y = 112

         y = 112÷16

         y = 7

∠ C = 5×(7) + 1 = 36°

∠ D = 11×(7) + 4 = 81°

∠ DEC = 180- 117 = 63°

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answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq

for this pair of functions g(x)=x-2 and f(x)=|x| is (g o f)(a)= |a| -2

step-by-step explanation:

g(x)=x-2

f(x)=|x|

(g o f)(a)=?

(g o f)(x)=g(f(x))

(g o f)(x)=g(|x|)

(g o f)(x)=|x|-2

(g o f)(a)=|a|-2