Find the missing angle for the irregular polygon. show your work.

Sum of the interior angles=900º

x=80º

∠A=110º

∠C=130º

∠E=125º

Step-by-step explanation:

The shape is a heptagon. Meaning, the sum of the interior angles is 180º(n-2) where n is the number of sides. So, 180º(7-2)=180º(5)=900º.

So, we can add up all the angles.

x+30º+140º+x+50º+115º+x+45º+140º+140º=900º

3x+660º=900º

3x=240º

x=80º

Then, we can substitute for ∠A, ∠C, and ∠E

∠A=80+30=110º

∠C=80+50=130º

∠E=80+45=125º

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