Question

figure rhom is a rhombus. $overline{ro}$ and $overline{hm}$ 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. what is true about $angle msr$? $\bigcirc$ it must be acute. $\bigcirc$ it must be a right angle. $\bigcirc$ it must be equal to $angle mrh$. $\bigcirc$ it must be equal to $angle rms$.

Explanation:

In a rhombus, the diagonals are perpendicular bisectors of each other. So, the angle formed by the intersection of the diagonals (∠MSR) is a right angle. Let's analyze the options:

• "It must be acute": A right angle is 90°, not acute (less than 90°), so this is incorrect.
• "It must be a right angle": By the property of a rhombus, diagonals are perpendicular, so ∠MSR is 90°, a right angle. This is correct.
• "It must be equal to ∠MRH": ∠MRH is an angle of the rhombus, and ∠MSR is a right angle; they are not necessarily equal.
• "It must be equal to ∠RMS": ∠RMS and ∠MSR are different angles in triangle RMS; ∠RMS is not necessarily equal to ∠MSR (unless the triangle is isoceles in a specific way, but the rhombus property gives ∠MSR as right angle, not based on this equality).

Answer:

It must be a right angle.