Answered

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In triangle XYZ, m∠Z > m∠X + m∠Y. Which must be true about △XYZ?

m∠X + m∠Z < 90°
m∠Y > 90°
∠X and∠Y are complementary
m∠X + m∠Y < 90°

Sagot :

sqdancefan

Answer:

  (d) m∠X + m∠Y < 90°

Step-by-step explanation:

You want to know what must be true of the angles in ∆XYZ, given Z > X + Y.

Angle sum

We know the sum of angles in the triangle is 180°. The given conditions let us write two expressions for Z:

  Z > X + Y

  Z = 180° -(X + Y)

Substituting for Z, we have ...

  180° -(X +Y) > X +Y

  180° > 2(X +Y) . . . . . . . . . . add (X +Y)

Dividing by 2 gives ...

  X + Y < 90° . . . . . . . matches choice D

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