Question

A gemstone in the shape of a rhombus has the measurements shown. Match the measures with the angles.

Answer 1

`A= 50`

`B = 90^\circ`

`C = 50^\circ`

`D = 40`

Explanation:

Given

See attachment for gemstone

Required

Determine A, B, C and D

The diagonals of a rhombus meet at
`90\ degrees.`

So:

`B = 90^\circ`

Divide the rhombus into two triangles (upper and lower).

Considering the lower triangle.

Since the two sides are equal (4mm), then the triangle is isosceles.

The base angle of an isosceles triangle
`are\ equal.`

So:

`C = 50^\circ`

Split the lower triangle into two, you get two right-angled triangles.

From one of these triangles, we have:

`C + D + 90 = 180`

`D = 180 - 90 - C`

`D = 180 - 90 - 50`

`D = 40`

Lastly, A and C are corresponding angles.

So:

`A = C`

`A= 50`