Question

if m angle 1= 53° , m angle 2=65°and m angle 3= 43° ,find measures of angle x and angle y. Justify your answer

Answer 1

Here given ,  ∠ AEB  =  ∠ 1 = 53° , ∠ EBD  =  ∠ 2  = 65° , ∠ BDC  =  ∠ 3 = 43° , ∠ BAE =  x , ∠CBD =  y and ∠ BCD = 90°

From angle sum property of triangle we get in ∆ BCD :

∠ BCD + ∠ BDC  +  ∠CBD =  180°  , Substitute all values and get

90° + 43° + y  = 180°

133°  +  y  =  180°

y  = 47°

We know : An  exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles.

So , In ∆ ABE we get 

∠ BAE  +  ∠  AEB  =  ∠ CBE  ,

∠ BAE +  ∠ AEB  =  ∠ EBD +  ∠ CBD ,

x +  ∠ 1  =  ∠ 2 +  y  , Substitute all values we get

x  + 53°  = 65°  + 47°

x  + 53°  = 112°

x  = 59° 

So, 

x  = 59°   and y =47°                                                          ( Ans ).


Hope it helps to you.

Answer 2

Given:∠ AEB  =  ∠ 1 = 53° , ∠ EBD  =  ∠ 2  = 65° , ∠ BDC  =  ∠ 3 = 43° , ∠ BAE =  x , ∠CBD =  y and ∠ BCD = 90°

From angle sum property of triangle we get in ∆ BCD :

∠ BCD + ∠ BDC  +  ∠CBD =  180°  , Substitute all values and get

90° + 43° + y  = 180°

133°  +  y  =  180°

y  = 47°

An  exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles.

So , In ∆ ABE we get 

∠ BAE  +  ∠  AEB  =  ∠ CBE  ,

∠ BAE +  ∠ AEB  =  ∠ EBD +  ∠ CBD ,

x +  ∠ 1  =  ∠ 2 +  y  , Substitute all values we get

x  + 53°  = 65°  + 47°

x  + 53°  = 112°

x  = 59° 

So,

x  = 59°   and y =47°