Question

In the given fig., AB=BC=AC=CD, then the measurement of x is:


please i need it be fast​

Answer 1

Answer:

Given

AB=BC=CA

If 3 sides of a triangle are equal then it's an equilateral triangle.

If so then their all angles are also equal

that is

ABC+BCA+CAB=180°(sum of all interior angles of a triangle are supplementary)

all are equal therefore,I can use any angle of the triangle in any other angle of it

ABC+ABC+ABC=180°

3 ABC=180

ABC=180/3

ABC=60°

therefore the angles in ∆ABC are

ABC=60°

BCA=60°

CAB=60°

but we've to find x

from the figure

ACB+ACD=180°(linear pair)

60+ACD=180

ACD=180-60

ACD=120°

also given AC=CD

if two oppositie sides of a triangle are equal then their opposite angles are also equal.

if so ,then

CAD=CDA

therefore

ACD+CAD+CDA=180°(sum of all interior angles of a triangle are supplementary)

CAD=CDA,so let them be x each

that is

120+x+x=180

2x=180-120=60

x=60/2

x=30°

then

CAD=CDA=x=30°

therefore the value of x is 30°

Answer 2

Answer:

ஃ, c) x = 30°

Step-by-step explanation:

Given, AB = BC = AC

y + y + y = 180° ( By angle sum property )

3y = 180°

$\sf y = \frac{\cancel{180}}{ \cancel{3}} = 60°$

60° + ∠C = 180° ( By linear pair )

∠C = 180° - 60° = 120°

Given, AC = CD

120° + x + x = 180° ( By angle sum property )

120° + 2x = 180°

2x = 180° - 120° = 60°

$\sf x = \frac{\cancel{60}}{ \cancel{2}} = 30°$

In this answer, we learnt:

• Angle sum property of a triangle

• Linear pair