Question

XYZ

is an equilateral triangle. The perpendicular from

X

to

YZ

meets

YZ

in

M

. The

perpendicular from

M

to

XZ

meets

XZ

at

N.

calculate

angle N.

Calculate

angle NMX​

Answer 1

60°

Explanation:

Triangle XYZ is equilateral triangle. In equilateral triangle all interior angles have measures of 60° each.

Line XM is perpendicular to the side YZ. Then this line is also an angle X bisector (the height of the equilateral triangle is also its median and angle bisector), so

m∠MXN = 30°

Consider triangle MNX. This is right triangle, because MN ⊥ XZ.

The sum of the measures of all interior angles in the triangle is always 180°, so

`m\angle MXN+m\angle MNX+m\angle NMX=180^(\circ)\\ \\30^(\circ)+90^(\circ)+m\angle NMX=180^(\circ)\\ \\m\angle NMX=180^(\circ)-30^(\circ)-90^(\circ)=60^(\circ)`