Question

(Help) Find the measure of the missing angle

Answer 1

68°

Explanation:

Remember :

• The diagonals of a rectangle are equal
• Hence, they will have equal angles on the corners of the shape

Solving :

• ∠DOA = ∠COB = 44° (Vertically Opposite Angles)
• Now, consider ΔDOA
• ∠ODA = ∠OAD (Because angles opposing equal side lengths are equal)
• ∠ODA + ∠OAD + ∠DOA = 180° (Angle Sum Property)
• 2∠OAD + ∠DOA = 180°
• 2∠OAD + 44° = 180°
• 2∠OAD = 136°
• ∠OAD = 68° (missing angle value)

Answer 2

Let the missing angle be x.

It should be noted:

• The two diagonals form four isosceles triangles. (ΔBOC, ΔCOD, ΔDOA, and ΔAOB)
• ∠DOA = ∠BOC = 44 (Vertically opposite angles)
• Interior angles of a triangle sum up to 180°

This means that...

• 44 + x + x = 180

Combine like terms.

• 44 + 2x = 180

Subtract 44 both sides.

• 2x = 180 - 44

Simplify the RHS

• 2x = 136

Divide 2 both sides.

• 2x/2 = 136/2
• => x = 136/2 = 68°