Assuming you need an answer to question #7, here it is.
The sum of all angles inside a polygon depends on the number of sides it has. (n-2) x 180°, where n is the number of sides. Knowing there are 5 sides to the polygon, we can figure out the sum of its interior angles : (5-2) x 180° = 3x180° = 540°
We know the values of the two right angles on the right side of the shape. They both are of 90° (aka right angle) and add up to 180°. This means that the other angles must make up the rest : 540° (Total) - 180° (right side) = 360° (total of angles A, B and C).
Now we need to make relations between these unknown angles. 1. A=B They were described as having the same size; 2. A=2C A and B were described as being twice as big as C, so we would need two times C to equal A; 3. A+B+C = 360° Which we figured out earlier.
Since B=A we can replace B in the third equation : A+A+C = 360° 2A+C = 360° We also know that A=2C : 2(2C)+C=360° 4C+C=360° 5C=360° We solve for C : C=72°
Now that we know the value of angle C, we can work our way up towards angles A and B. A=2C A=2(72°) A=144°
B=A B=144°
We can verify our values to see if it all makes sense. Is A+B+C=360° still true? 144°+144°+72°=360° 360°=360°
Thus, angles A, B and C are respectively 144°, 144° and 72°.
