# PROBLEMS ON EXTERIOR ANGLES OF A TRIANGLE

An exterior angle of a triangle is equal in size to the sum of its interior opposite angles Problem 1 :

Find the unknown Solution :

Using exterior angle theorem,

y + 80  =  125

y  =  125-80

y  =  45

Problem 2 :

Find the unknown. Solution :

Using exterior angle theorem,

x + 80  =  3x

2x  =  80

x  =  40

Problem 3 :

Find the unknowns. Solution :

In triangle, the sum of interior angles is 180 degrees.

a + 2a + 90  =  180

3a+90  =  180

3a  =  90

a  =  30

To find the value of b, we can use any of the way given below.

 a+90  =  bApplying the value of a30+90  =  bb  =  120 Using linear pair2a+b  =  1802(30)+b  =  18060+b  =  180b  =  120

In both ways, the answer will be same.

Problem 4 :

Find the unknowns. Solution :

By observing the figure, it is a isosceles triangle.

<CAB  =  <CBA

<CBA + <CBD  =  180

<CBA + 112  =  180

<CBA  =  180 - 112

<CBA  =  68

In triangle ABC,

<ACB + <CAB + <CBA  =  180

p + 68 + 68  =  180

p + 136  =  180

p  =  180 - 136

p  =  44

Problem 5 :

Find the unknowns. Solution :

The given triangle ABC is a isosceles triangle.

<ABC  =  <ACB  =  2x

2x + 118  =  180

2x  =  62

x  =  31

<ABC + <BCA + <CAB  =  180

2x+y+2x  =  180

4x+y  =  180

4(31) + y  =  180

124 + y  = 180

y  =  56

Problem 6 :

Find <LMN and <MLN. Solution :

<LMN + <MLN  =  <LNP

x+2x  =  108

3x  =  108

x  =  108/3

x  =  36

<LMN  =36

<MLN  =  2(36)

<MLN  =  72 Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

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