Question

one angle of a triangle is the sum of its two other angles . if one of these two angles is half of third angle find all the angles of the triangle
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Answer 1

Let,

One angle = x

Other two angles be y and z

One angle of a triangle is the sum of its two other angles.

• y + z = x

One of these two angles is half of third angle.

One angle is y and other x

• x/2 = y

• z + x/2 = x [y = x/2]

Sum of all angles of triangle = 180°

=> x + z + x/2 = 180°

• z + x/2 = x

=> x + x = 180°

=> 2x = 180°

=> x = 180°/2

=> x = 90°

Finding value of y

=> y = x/2

=> y = 90/2

=> y = 45°

Finding value of z

=> z + x/2 = 90°

=> z + 90°/2 = 90°

=> z + 45° = 90°

=> z = 90° - 45°

=> z = 45°

All angles are 90°, 45° and 45°

Answer 2

Answer:

x = 90°

y = 60°

z = 30°

Step-by-step explanation:

Let's say that the first angle is x and the second angle is y and the third angle is z.

We have three equations we extract from this question :

1. x = y + z
2. y = z/2
3. x + y + z = 180° (Angle sum property of a triangle)

Now, we can start substituting.

Since, we know that y = z/2 we can substitute in this equation :

x = y + z

∴ x = z/2 + z = (z + 2z)/2 (LCM)

∴ x = 3z/2

Now, we know that :

• x = 3z/2
• y = z/2

Now, we substitute in this equation :

x + y + z = 180°

(3z/2) + (z/2) + z = 180°

6z/2 = 180° (LCM)

6z = 180 × 2 = 360° (transposition)

z = 360/6 = 60°

And then, we substitute in the equations we know about x and y.

x = 3z/2 = 3 × 60 ÷ 2 = 90°

y = z/2 = 60 ÷ 2 = 30°

∴ x = 90°

  y = 60°

  z = 30°