Answer:
∠1 = 36°
∠2 = 72°
∠3 = 72°
∠4 = 72°
∠5 = 36°
Step-by-step explanation:
The angles of rhombus are ∠1 = 36°, ∠2 = 72°, ∠3 = 72°, ∠4 = 72°, ∠5 = 36°.
A rhombus is a quadrilateral with four equal sides and opposite equal angles. It has two diagonals that bisect each other at right angles. It also has opposite sides parallel and the sum of all the four interior angles is 360 degrees.
For the given situation,
From the diagram of rhombus,
The angle is 72°.
In rhombus,
Opposite angles are equal.
So, [tex]\angle2 = \angle3 = \angle4[/tex] are equal to [tex]\angle72[/tex].
Diagonals bisect the angles and the sum of two adjacent angles is equal to 180 degrees.
⇒ [tex]\angle D + \angle E = 180[/tex]
Here, [tex]\angle D = \angle 72 + \angle 72[/tex]
⇒ [tex]\angle D = \angle 144[/tex]
Thus, [tex]\angle E = \angle 180 -\angle 144[/tex]
⇒ [tex]\angle 1 = \angle 36[/tex]
we know that, [tex]\angle E = \angle G[/tex]
⇒ [tex]\angle 5 = \angle 36[/tex]
Hence we can conclude that the angles of rhombus are ∠1 = 36°, ∠2 = 72°, ∠3 = 72°, ∠4 = 72°, ∠5 = 36°.
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