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प्रश्न
Determine the measure of each of the equal angles of a right-angled isosceles triangle.
ABC is a right-angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.
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उत्तर
Given to determine the measure of each of the equal angles of right– angled isosceles triangle
Consider on a right – angled isosceles triangle ABC such that
∠A = 90° and AB = AC
Since, AB = AC ⇒ ∠C = ∠B ……….(1)
[Angles opposite to equal sides are equal] Now,
Sum of angles in a triangle = 180°
∠A + ∠B +∠C = 180°
⇒ 90° + ∠B + ∠B = 180° [ ∴∠A = 90° and ∠B = ∠C ]
⇒ 2∠B = 90°
⇒ ∠B = 45°⇒ ∠C = 45°
∴ ∠B =∠C = 45°
Hence, the measure of each of the equal angles of a right-angled isosceles triangle is 45°.
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