Question

(i) If one angle of the parallelogram is 75, find the other three angles.

Answer 1

Answer:

95°, 95°, 95°

Step-by-step explanation:

One angle of a parallelogram = 75°

Let all the other three angles be 'x'.

We all know that Sum of interior angles of a parallelogram = 360°

A parallelogram has 4 angles so,the angles are: 75°, x°, x°, x°

Then, 75°+x°+x°+x° = 360°

After solving the equation,

75° + 3x = 360°

3x = 360° - 75°

3x = 285

x = 285 ÷ 3

x = 95°

Since x = 95°,

Angles of a parallelogram = 75°, 95°, 95°, 95°

CHECK:

Sum of interior angles of a parallelogram = 360°

75° + 95° + 95° + 95° = 360°

360° = 360°

LHS = RHS

H.T.P. (Hence the proof)