Word Problem 3
Problem 3: What is the measure of angle at corner ‘A’ of the star shape ?
Though we are given simply ‘A’ corner, we name B, E, C,F, G and D points by our self. Now A to D is a straight line, and we know that angle on a straight line is 180 degrees. So if we subtract 110 from 180 then angle <AFG will be 70 degrees . Now BFG is a triangle and we know the sum of angles in a triangle is 180 degrees. So, sum of two angles of this triangle is 70+40=110, the third angle will be 70 degrees i-e the angle <BGF is 70 degrees measure. Reciprocal of angle < BFG is the angle<AGE it will be 70 degrees as well. Similarly reciprocal of angle <AED is the angle <AEC which will be 110 degrees as well. Again D to C point is straight line , if we subtract 110 from 180 then the angle <AEG is 70 degrees.
So, finally two angles of triangle AEG are of 70 degrees each . The third angle will be 180-70-70=40 degrees