MathMatrix

We’re given the following triangle, with angles a, b, c, d and e as shown. We’re required to find the value of a+b+c+d+e.

Solution

Consider Triangle △ABC as shown. Then extend the line AC to Z.

∠ZAB is exterior angle to △ABC

Hence, Using Exterior angle Theorem we get:

∠ZAB = b + d . . . 1

Similarly, consider another △PQR, and extend the line QR to Z.

∠ZQP is exterior angle to △PQR

Using Exterior angle Theorem we get:

∠ZQP = c + e . . . 2

Now, consider △ZAQ

∠ZAQ + ∠AZQ + ∠AQZ = 180° (Angle Sum Property of Triangle)

(b + d) + (a) + (c + e) = 180°

OR

a + b + c + d + e = 180°

That’s our answer!!