Question

The exterior angles obtained on producing the base of a
triangle both ways are 100° and 120°.
Find all the angles.

Answer 1

Answer:

Let ABC be the triangle with BC produced on both sides B and C till E and F respectively.

Angle ABE = 100 degrees

Angle ACF = 120 degrees

angle ABE + angle ABC = 180 degrees

=> 100 degrees+angle ABC=180degrees

=> angle ABC = (180-100) degrees

=> angle ABC = 80 degrees

angle ACF + angle ACB = 180 degrees

=> 120 degrees+angle ACB=180 degrees

=> angle ACB = (180-120) degrees

=> angle ACB = 60 degrees

angle BAC = (180-80-60) degrees

= (180-140) degrees

= 40 degrees

So, the three angles are 80,60,40 degrees.

                OR

LET CDE BE THE GIVEN TRIANGLE

WITH DE PRODUCED TO BOTH SIDES TILL A AND B

ANGLE CDA = 100

ANGLE CEB = 120

ANGLE CDA + ANGLE CDE = 180 (LINEAR PAIR)

ANGLE CDE = 80

ANGLE CEB + ANGLE CEB = 180 (LINEAR PAIR)

ANGLE CEB = 60

SO THIRD ANGLE DCE = 180-80-60

DCE = 40

Hope it helps....

Answer 2

Answer:

2 exterior Angeles are 100° and 120°

2 interior angle forming exterior =180°-100° and 180°-120°

<A=80°.

<B=60°

<C=180°-(80°+60°)

[According to angle sum property of triangle]

<C=180°-(140°)

<C=40°

All angles are 80°,60°,40°