m∠X + m∠Z < 90°
m∠Y > 90°
∠X and∠Y are complementary
m∠X + m∠Y < 90°
Since the given is m<Z > m<X +m<Y and the sum of measure of angles of a triangle is equal 180 degrees so from this result that the last one choice need being true sure so m<X +m<Y < 90°
For the triangle xyz, m∠z > m∠x + m∠y the total internal angles of a triangle is 180, therefore, m∠x + m∠y < 90° is a true statement.
The sum of angles in a triangle is equals to 180 degrees.
Therefore, if the angles of a triangle are x, y and z,
x + y + z = 180 degrees
If m∠z > m∠x + m∠y,
Therefore, m∠x + m∠y the two other angles should be less than 90 degrees.
Hence,
m∠x + m∠y < 90°
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