Question

Find the measure of the missing angles in the rhombus.

Answer 1

Let me sketch the rhombus, Then solve,

Let's find angle 1,

we know that triangle DCB is an isosceles triangle with one base angle equal to 55 degrees.

But in an isosceles triangle, both base angles are equal, so:

`\angle1=55^o`

Let's find angle 3,

Since the figure is a rhombus, we know that the diagonals of a rhombus bisect at 90 degrees, thus

`\angle3=90^o`

Let's find angle 2,

I will be sketching triangle ACO separately to find angle 2,

We know that since the diagonals bisect at right angles, we would have a right angled triangle in ACO. and since both the 55 degree and the angle "2" should add up to 90 degrees, we have:

`\begin{gathered} \angle2=90-55 \\ \angle2=35^o \end{gathered}`

Therefore angle 2 = 35 degrees

iv. Now to angle BDC .

We know that all the angles in that triangle should add to 180 degrees, so,

So