Question

∆ABC (Fig. 1) is isosceles and D is the mid point of base BC.
(i) Why is ∆ABC ≌ ∆ACD?
(ii) If m ∠B=(2x+15)° and m ∠C=55° find the value of x.

Please answer the questions with correct explanation
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Answer 1

Answer:

x = 20

Step-by-step explanation:

∠B = ∠C

∠C = 55°

∠B = (2x+15)°

2x+15 = 55°

2x = 40

x = 20

Answer 2

Answer:

since triangle ABC is ISOCELES

AB=AC

Angle ABC=ACB

(i) In triangle ABC and ACD

AB=AC

Angle ABC=ACD

AC=AC__(COMMON SIDE)

thus

triangle ABC ~ ACD

That is , Triangle ABC is congruent to ACD

(ii) angle B=C

angle B=2x+15

angle C=55

thus

2x+15=55

2x=55-15

x=40/2

x=20