Question

In kite WEAR, ∠WEA = 70° and ∠ARW = 80°. Find the remaining two angles.

Answer 1

Given, In a kite WEAR, ∠WEA = 70°, ∠ARW = 80°

Now, by the interior angle sum property of a quadrilateral,

∠RWE + ∠WEA + ∠EAR + ∠ARW = 360°

⇒ ∠RWE + 70 + ∠EAR + 80° = 360°

⇒ ∠RWE +  EAR = 360° – 150°

⇒ ∠RWE + ∠EAR = 210°  ...(i)

Now, ∠RWA = ∠RAW   [∵ RW = RA]  ...(ii)

And ∠AWE = ∠WAE   [∵ WE = AE]  ...(iii)

On adding equations (ii) and (iii), we get

∠RWA + ∠AWE = ∠RAW + ∠WAE

⇒ ∠RWE = ∠RAE

From equation (i),

 2∠RWE = 210°

∠RWE = 105°

⇒ ∠RWE = ∠RAE = 105°