Question

(i) If one of the angles of a parallelogram measures 75°, find the other angles.​

Answer 1

Answer:

75, 105, 105

Step-by-step explanation:

Adjacent angles are supplementary. 180-75=105

alternate angles are equal    75=75 ; 105=1-5

Answer 2

Question:

If one of the angles of a parallelogram measures 75°, find the other angles.​

Given:

In parallelogram ABCD

∠A = 75°

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To Find:

• ∠B

• ∠C

• ∠D

Theorem Used:

• Opposite angles of a parallelogram are equal

• Angles adjacent in a parallelogram are supplementary

Solution:

In parallelogram ABCD

∠A = 75°

To Find the other angles

Finding ∠C ,

∠A = ∠C = 75° ( Opposite angles of a parallelogram are equal )

Finding ∠B ,

∠A + ∠B =180° ( Angles adjacent in a parallelogram are supplementary )

∠A + ∠B =180°

75° + ∠B =180°

∠B = 180 - 75

∠B = 105°

Finding D,

∠B  = ∠D= 105° ( Angles adjacent in a parallelogram are supplementary )

Therefore the angles are  :

• ∠A = 75°

• ∠B  = 105°

• ∠C = 75°

• ∠D = 105°

Check:

∠A +∠B+∠C+∠D = 360°( Sum of all angles of a quadrilateral = 360)

75° + 105° + 75° + 105° = 360°

180° + 180° = 360°

360° = 360°

L.H.S = R.H.S

Answer:

• ∠A = 75°

• ∠B  = 105°

• ∠C = 75°

• ∠D = 105°

For extra information refer to: https://brainly.in/question/22395431

Prove that in a parallelogram, opposite sides are equal.​-https://brainly.in/question/14945970

Sum of all angles of a quadrilateral = 360- https://brainly.in/question/4910647