Question

2. In the given figure find x+y+z
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Answer 1

Answer:

if this triangle is a equilateral triangle.

then,

x=y=z=120°

so,

120°+120°+120°=360°

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Answer 2

Answer:

The value x+y+z = 360°

Step-by-step explanation:

Given,

Δ ABC with exterior angles of the triangle are x,y, and z

To find,

The value x+y+z

Solution:

Recall the theorems

Angle sum property:

Sum of three angles of a triangle = 180°

Exterior angle theorem:

The exterior angle of a triangle is equal to the sum of its interior opposite angles

From the attached diagram we have,

The interior opposite angles of 'x' are ∠A and ∠B

The interior opposite angles of  'y' are ∠C and ∠B

The interior opposite angles of  'z' are ∠A and ∠C

Then by exterior angle theorem, we have

x = ∠A + ∠B

y = ∠C + ∠B

z = ∠A + ∠C

x+y+z = ∠A + ∠B +∠C + ∠B + ∠A + ∠C

= 2∠A + 2∠B +2∠C

= 2(∠A + ∠B +∠C)

By angle sum property of triangle we have, ∠A + ∠B +∠C = 180

=  2× 180

= 360°

∴ The value x+y+z = 360°

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