Question

The two sides of a triangle are equal and angles opposite to them are 40° and x. Find x.
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Answer 1

Answer:

ABC is a given triangle with, AB=AC.

To prove: Angle opposite to AB= Angle

opposite to AC (i.e) ∠C=∠B

Construction: Draw AD perpendicular to BC

∴∠ADB=∠ADC=90

o

Proof:

Consider △ABD and △ACD

AD is common

AB=AC

∴∠ADB=∠ADC=90

o

Hence ∠ABD=∠ACD

∠ABC=∠ACB

∠B=∠C. Hence the proof

This is known as Isosceles triangle theorem

Answer 2

40°

Step-by-step explanation:

Q.

The two sides of a triangle are equal and angles opposite to them are 40° and x. Find x.

Solution -

You are talking about a isosceles triangle.

A common rule, you should remember -

The opposite angles of equal sides of isosceles triangle are equal.

So here,

40° and x are opposite angles of equal sides of isosceles triangle, (see the attachment)

=> x = 40°

Hence the value of x is 40°

hope it helps.