Question

pls give me the ans in step by step i am unable to understand this question
question is in image form​

Answer 1

Answer:

answers..

Step-by-step explanation:

(a) we know that angle opposite to equal lines are equal...so let angle between x and y be z.. this z is equal to the third angle of the triangle which means that

50+z+z=180

50+2z=180

2z=130

z=65

Now take case of x here we know that

x+40=50(exterior angle prop.)

so, x=10

now x+y+z=180, linear pair

10+65+y=180

y=180-75

y=105

(b) let opposite angles of 50 be z and z

in previous question we found that angle opp. ti equal sides are equal..and also found that

z=65

now, x=50+z(exterior angle prop)

y=50+z("""'''''''')

so both are equal

x=y=50 +z

=50+65

=115.

(c) here angle opp.to 65 both are equal because of the reason mentioned before....

therefore..

x+x+65=180(angle sum prop.)

2x+65=180

2x=115

x=115/2

x=57.5

(d) here take the triangle inside...we can find one of its angle like this...

let that angle be y

116+y=180(linear pair )

y=180-116

y=64

now take the remaining angles of that triangle.. we know that these remaining once are equal because of the reason mentioned in first qstn..so let it be z

z+z+64 = 180, angle sum property...

2z +64=180

2z=180-64

2z=116

z=116/2

z=58

now we know that z+x=180

therefore 58+x=180

x=180-58

x=122

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