The answers of the geometry exercise are :
1.) x = 25° ;
2.) x = 129°
3.) x = 73° ; y = 107° ; z = 73°
4.) s = 167°
5.) s = 52°
6.) M1 = 109° ; M2 = 79°
7.) M2 = 84°
1.)
The angle is right angled, which means the angle equals 90°
Hence,
x° + 65° = 90°
x = 90° - 65°
x = 25°
2.)
Vertically opposite angles are the same ; and the sum of angles at a point is 360°
Hence,
(51° × 2) + (2x) = 360°
102° + 2x = 360°
2x = 360° - 102°
2x = 258°
x = 258° / 2
x = 129°
3.)
y = 107° (Vertically opposite angles)
z = x (vertically opposite angles)
z = 2x
2x + (2 × 107) = 360°
2x + 214 = 360
2x = 360 - 214
2x = 146
x = 146 / 2
x = 73°
x = z = 73°
4.)
Let second angle = s
(s + 13) = 180 (Supplementary angles sums up to 180°)
s = 180 - 13 = 167°
5.)
Let second angle = s
(s + 38) = 90 (Complementary angles sums up to 90°)
s = 90 - 38 = 52°
6.)
Sum of Linear pair of angles = 180°
Hence,
(5x + 9) + (3x + 11) = 180
5x + 9 + 3x + 11 = 180
8x + 20 = 180
8x = 180 - 20
8x = 160
x = 20°
M1 = (5(20) + 9) = 100 + 9 = 109°
M2 = (3(20) + 11) = 60 + 11 = 71°
7.)
M1 = M2 (vertical angles are equal)
(17x + 1) = (20x - 14)
17x - 20x = - 14 - 1
-3x = - 15
x = 5
M2 = (20(5) - 14) = 100 - 14 = 84°
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