Question

Value of x in the figure below is:

a) 20o

b) 40o

c) 80o

d) 160o​

Answer 1

Answer:

x= 40°

We can solve it by two methods ;

let ABC be the triangle and D is extended part or line

Angle ABC=60°

ANGLE BAC=X

ANGLE DCA= 100°

method 1;

ANGLE DCA +ANGLE ACB=180°( linear pair axiom)

100° +ANGLE ACB= 180°

ANGLE ACB= 180°-100°

ANGLE ACB=80°

NOW, WE KNOW THAT THE SUM OF ALL THE ANGLES OF A TRIANGLE IS 180° ,

SO, ACB+ABC+ BAC=180°

80°+60°+x= 180°

x= 180°- 140°

x= 40°

method 2;

the sum of two internal angle is equal to the opposite exterior angle

so, angle BAC+angle ABC= ANGLE DCA

X= 100°-60°

X= 40°

Answer 2

Answer:

40 degree is the value of x in the figure given below.

Step-by-step explanation:

we can name the third angle of the triangle = y

Now

$100+y = 180$  (sum of linear angles is 180 degree)

$y = 180-100\\y= 80$

now the sum of all angles of a triangle is 180 degrees.

so

$∠y + 60 +∠x=180$

$80 + 60 +x =180$

$140 +x =180\\x =180-140\\x=40$

Hence, the value of x is 40 degrees.