Question

In triangle ABC, AB = BC, measure of angle A = 50 degree. Then the measures of angle B and angle C are -----degree and ...... degree respectively.

Answer 1

Answer :

In triangle ABC, AB = BC, measure of ∠A = 50 degree. Then the measures of ∠B and ∠C are 65° degree and 65° degree respectively.

Step-by-step explanation :

Given that,

AB = BC, and figure,

$\setlength{\unitlength}{1.2 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\qbezier(5,0)(5,0)(3,3)\qbezier(5,0)(1,0)(1,0)\put(2.85,3.2){ \bf C }\put(0.5,-0.3){ \bf A }\put(5.2,-0.3){ \bf B }\qbezier(1.56,0)(1.7,0.3)(1.3,0.5)\put(1.7,0.3){ \bf 50^{\circ} }\end{picture}$

Solution :

∠A + ∠B + ∠C = 180° ......Angle sum property of triangle

Given that, AB = AC therefore, ∠B = ∠C

Let us assume ∠B as x and ∠C as x,

➨ 50° + x + x = 180°

➨ 50° + 2x = 180°

➨ 2x = 180 - 50

➨ 2x = 130

➨ x = 130 / 2

➨ x = 65

Hence, ∠B = ∠C = 65°

Now, Verification

∠A + ∠B + ∠C = 180°

By putting the values,

➨ 50° + 65° + 65° = 180°

➨ 115 + 65 = 180

➨ 180 = 180

L.H.S = R.H.S

Hence, Verified !