Question

Figure RHOM is a rhombus. Line segment R O and Line segment H M are the diagonals of the rhombus, as well as angle bisectors of the vertex angles, and they create four isosceles triangles: HOM, MHR, RHO, and OMR.

Rhombus R H O M has all equal side lengths. Lines are drawn from each point to point S at the center.

What is true about AngleMSR?

It must be acute.
It must be a right angle.
It must be equal to AngleMRH.
It must be equal to AngleRMS.

Answer 1

It must be a right angle.

Reason: SM and SR lie along the diagonals HM and RO. In a rhombus the diagonals bisect each other and are perpendicular, so they meet at S at 90°. Hence ∠MSR = 90°.