Math, asked by Anonymous, 9 months ago

Please help... otherwise irrelevant answers will be reported .​

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Answered by EthicalElite
45

1.) Let angle= x

other two angles= y and z

By using angle sum property of triangle.

x+y+z=180

We are given that one angle is the sum of other two angles.

So, we can write y+z= x

x+x=180

2x=180

x=  \frac {180}{2}

x=90

 \boxed {Hence, \: proved}

______________________________________

2.) By angle sum property of triangle:-

∠A + ∠B + ∠C= 180°

60° + 70° + ∠C= 180°

130° + ∠C= 180°

∠C= 180°-130°

 \boxed {∠C= 50°}

As, ∠B is corresponding to ∠D

Therefore,

∠B= ∠D

70°= ∠D

 \boxed {∠D= 70°}

As, ∠C is corresponding to ∠E

Therefore,

∠C= ∠E

50°= ∠E

 \boxed {∠E= 50°}

Therefore, ∠C= 50°, ∠D= 70° and ∠E= 50°

______________________________________

3.) As y and 70° are linear pair

Therefore,

y+70°= 180°

y= 180°-70°

 \boxed {y= 110°}

Let an angle z to be present on third angle of this triangle.

Therefore, by Angle sum property:-

y+40°+z= 180°

110°+40°+z= 180°

150°+z= 180°

z= 180°-150°

 \boxed {z= 30°}

As, z and x are linear pair

Therefore,

z+x= 180°

30°+x= 180°

x= 180°-30°

 \boxed {x= 150°}

Therefore, value of x= 150° and y= 110°

Answered by Anonymous
13

1.) Let angle= x

other two angles= y and z

By using angle sum property of triangle.

x+y+z=180

We are given that one angle is the sum of other two angles.

So, we can write y+z= x

x+x=180

2x=180

x=

x=90

_____________________

2.) By angle sum property of triangle:-

∠A + ∠B + ∠C= 180°

60° + 70° + ∠C= 180°

130° + ∠C= 180°

∠C= 180°-130°

As, ∠B is corresponding to ∠D

Therefore,

∠B= ∠D

70°= ∠D

As, ∠C is corresponding to ∠E

Therefore,

∠C= ∠E

50°= ∠E

Therefore, ∠C= 50°, ∠D= 70° and ∠E= 50°

_____________________

3.) As y and 70° are linear pair

Therefore,

y+70°= 180°

y= 180°-70°

Let an angle z to be present on third angle of this triangle.

Therefore, by Angle sum property:-

y+40°+z= 180°

110°+40°+z= 180°

150°+z= 180°

z= 180°-150°

As, z and x are linear pair

Therefore,

z+x= 180°

30°+x= 180°

x= 180°-30°

Therefore, value of x= 150° and y= 110°

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