Answer:
1. Right Triangle:
A right triangle has one right angle (90 degrees) and the sum of all angles in any triangle is 180 degrees. Therefore, the other two angles must add up to 90 degrees.
[tex] \text{Angle 1} = 90^\circ[/tex]
[tex]\text{Angle 2} = x^\circ[/tex]
[tex] \text{Angle 3} = y^\circ[/tex]
[tex]x + y = 90^\circ[/tex]
[tex]\text{Sum} = 180^\circ[/tex]
2. Triangle:
For any general triangle, the sum of the interior angles is always 180 degrees.
[tex] \text{Angle 1} = x^\circ[/tex]
[tex]\text{Angle 2} = y^\circ[/tex]
[tex]\text{Angle 3} = z^\circ[/tex]
[tex]x + y + z = 180^\circ[/tex]
[tex]\text{Sum} = 180^\circ[/tex]
3. Rectangle:
A rectangle has four right angles, each measuring 90 degrees.
[tex] \text{Angle 1} = 90^\circ[/tex]
[tex] \text{Angle 2} = 90^\circ[/tex]
[tex] \text{Angle 3} = 90^\circ[/tex]
[tex] \text{Angle 4} = 90^\circ[/tex]
[tex] \text{Sum} = 360^\circ[/tex]
4. Trapezium (Trapezoid in American English):
A trapezium has two pairs of non-parallel sides but the sum of its interior angles is always 360 degrees.
[tex] \text{Angle 1} = x^\circ[/tex]
[tex] \text{Angle 2} = y^\circ[/tex]
[tex] \text{Angle 3} = z^\circ[/tex]
[tex]\text{Angle 4} = w^\circ[/tex]
[tex]x + y + z + w = 360^\circ[/tex]
[tex]\text{Sum} = 360^\circ[/tex]
5. Irregular Convex Pentagon:
The sum of the interior angles of a pentagon (regardless of its irregularity) is always given by (n-2) x 180) degrees, where (n) is the number of sides. For a pentagon, (n=5).
[tex] \text{Angle 1} = x^\circ[/tex]
[tex] \text{Angle 2} = y^\circ[/tex]
[tex] \text{Angle 3} = z^\circ[/tex]
[tex] \text{Angle 4} = w^\circ[/tex]
[tex] \text{Angle 5} = v^\circ[/tex]
[tex]x + y + z + w + v = 540^\circ[/tex]
Sum = 540°
