Question

If the sum of seven exterior angles is 200 degrees, find the sum of the eight interior angles not adjacent to these exterior angles.

Answer 1

, exterior angle + interior adjacent angle = 180° [Linear pair] Applying relation for polygon having n sides Sum of all exterior angles + Sum of all interior angles = nx 180° Sum of all exterior angles = nx 180° - Sum of all interior angles =n× 180° - (n-2) × 180° [Sum of interior angles is = (n - 2) x 180°] ning A

nx 180° - nx 180° +2 x 180° = 180°n - 180°n + 360°

= 360°

Sum of four exterior angles is 360°

15. In Figure, the bisectors of ZA and ZB meet at a point P. If ZC =100° and ZD= 50°, find the measure of ZAPB. D

50°

100⁰

A

B

Solution:

We know that Sum of angles of a quadrilateral is = 360°

In the quadrilateral ABCD

Given, ZC 100° and ZD= 50° ZA + 2B + ZC + ZD=360

Answer 2

Given ,

Sum of 7 exterior angles=200°

We know ,

Sum of exterior angles=360°

Therefore ,

Sum of Eighth angle=360°-200°=160°

MARK AS BRAINLIEST