Answer:
1 = 130° , 2 =50° , 3 = 85°, 4=45°
Step-by-step explanation:
1 =45 + 85 = 130 { sum of opposite interior angle equals exterior angle}
2 = 180 - 1 { angles on a straight line equals 180}
= 180 -130 = 50°
4 = 180 - 135 = 45° { angles on a straight line equals 180}
3 = 135 -2 { sum of opposite interior angles equals exterior angle; 3 + 2 = 135}
3 = 135-50 = 85°
Note : sum of opposite interior angles equals external exterior angle, let's prove it:
If we look at the triangle at the bottom left, we have :
85, 45 and r { let's denote r as the missing angle}
So 85 + 45 + r = 180° { sum of angles of a triangle}
By simple arithmetic
r = 180 - ( 85+45) = 180 - 130 = 50°
but r + 4 = 180° { sum of angles in a straight line equals 180°}
4 = 180 - 50 = 130°
So you see 4 is the exterior angle of the triangle opposite to 85° and 45° interior angles}
