A picture frame is shaped as a heptagon. The measure of one angle is 144°. The remaining interior angles are congruent. What is the measure of each remaining interior angle in the picture frame?

126°
180°
174°
150°

Question

A picture frame is shaped as a heptagon. The measure of one angle is 144°. The remaining interior angles are congruent. What is the measure of each remaining interior angle in the picture frame? 

 126° 
 180° 
 174° 
 150°

parthkohli · Answer

Heptagon is a polygon with seven number of sides(and angles).
Hint given.

anonymous · Answer

I'm sorry, I'm still lost.

parthkohli · Answer

OK, Imma help.$$Sum~of~angles = 180(n - 2) \text{ if there are }n \text{ sides.}  $$

parthkohli · Answer

So, if there are 7 sides, then the sum will be$$180(7 - 2) \implies 180 \times 5 \implies \cdots $$

parthkohli · Answer

What is $180 \times 5$?

anonymous · Answer

900

parthkohli · Answer

Good job. We now know that the sum of angles will be $900^{\circ}$, and that the angles are $144,x,x,x,x,x,x$.

parthkohli · Answer

This implies that $144 + x + x + x + x + x+x =900$ because all the other angles are equal.

parthkohli · Answer

Solve the equation.

anonymous · Answer

Thanks :)