Question

One of the angles of a triangle is 80° and the other two angles are equal. Find the

measure of each of the equal angles.
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Answer 1

Diagram:

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\qbezier(5,0)(5,0)(3,3)\qbezier(5,0)(1,0)(1,0)\put(2.85,3.2){ \bf A }\put(0.5,-0.3){ \bf C }\put(5.2,-0.3){ \bf B }\end{picture}$

Given:

• One of the angle = ∠A = 80°
• ∠B = ∠C = x°

To find:

1. ∠B = ?
2. ∠C = ?

Method:

Remember:

→ The Sum of all angles in any Triangle is always 180°. This is known as Angle Sum Property.

Applying the above property;

∠A + ∠B + ∠C = 180°

⇒ 80° + x + x = 180°

⇒ 80° + 2x = 180°

⇒ 2x = 180° - 80°

⇒ 2x = 100°

⇒ x = 100° ÷ 2

⇒ x = 50°

∴ The measure of each angles = 80°, 50° and 50°