DM – rhombus height ABCD, angle BDM = 40 °. Find angle A.

Since DM is the height of the rhombus, triangle BDM is rectangular. The sum of the angles BDM and MBD is

90 ° means <MBD = 90 ° – <BDM = 90 ° – 40 ° = 50 °;

BD is the diagonal of the rhombus ABCD;

The diagonal of the rhombus divides the angle in half, which means <CBD = <DBA;

The CBD angle is the MBD angle; <B = 2 * <MBD = 2 * 50 ° = 100 °;

The sum of the angles of the rhombus is 360 °;

<B = <D; <A = <C; <A = (360 ° – 2 * <B) 2 = (360 ° – 2 * 100 °) 2 = 80 °.