Question

What is the value of x in the rhombus below?

Answer 1

Answer:

Option C

$21\°$

Step-by-step explanation:

we know that

The two diagonals of a rhombus are perpendicular

so

Let

O------> the center of the rhombus

m∠AOB=$90\°$

Remember that

The sum of the internal angles of a triangle is equal to $180\°$

therefore

in the triangle AOB

m∠AOB+m∠OAB+m∠OBA=$180\°$

substitute the values

$90\°+(2x+1)\°+(2x+5)\°=180\°$

solve for x

$(4x+6)\°=90\°$

$4x=90\°-6\°$

$x=21\°$

Answer 2

Look into my attachment

in rhombus ABCD, ∠AOB = 90°

Look at ΔAOB
the sum of inner angles = 180°
∠BAO + ∠AOB + ∠ABO = 180°
2x + 1 + 90 + 2x + 5 = 180°
4x + 96 = 180
4x = 84
x = 21