Q3 of 28 Page 84

In Δ ABC, the measure of ∠A is greater than the measure of ∠ B by 24° . If exterior angle ∠C is 108°. Find the angles of the Δ ABC.

Theorem 2:


If a side of a triangle is produced, the exterior angle so formed, is equal to the sum of the two interior angle.


Let the ∠B be x.


∴ ∠ B = x


∴ ∠ A = ∠ B + 24°


= x + 24°



Ext. [T2] ∠ C = ∠ B + ∠ A


⇒ 108° = x + x + 24°


⇒ 108° = 2x + 24°


⇒ 2x = 108° - 24°


⇒ 2x = 84°


⇒


⇒ x = 42°


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