Question

(4) Sum of two angles of a triangle is 90° and their difference is 50°. Find all angles​

Answer 1

Answer:

70°, 20°, and 90°

Step-by-step explanation:

Let the angles be x and y respectively.

∴By conditions,

A.  x+y = 90 ...........(1)

B.  x-y = 50  ...........(2)

Using elimination method, solve for x:

Adding (2) to (1):

        x+y=90

  (+)  x-y=50

------------------------------

        2x  = 140

∴ x=70

Substituting x in (1):

70 + y = 90

∴ y = 20

∴ Angle 1 = x = 70°

  Angle 2 = y = 20°

Solve for Angle 3:

Angle 1 + Angle 2 + Angle 3 = 180° ............. Angle sum property of triangles.

70° + 20° + Angle 3 = 180°

Angle 3 = 180° - 90°

∴ Angle 3 = 90°

∴ The angles of the triangle are 70°, 20°, and 90° respectively.

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Answer 2

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