Question

Find the values of the unknowns x, y, z in the given parallelograms:
(a)
(b)
у
X
z
75°
z
70°​

Answer 1

$\Large \mathfrak \orange {✽ \: Question \: ✽}$

Find the values of the unknown x, y, z in the parallelogram.

$\Large \mathfrak \orange {✽ \: Solution \: ✽}$

We know that in a parallelogram opposite angles are equal, so :

<y = 75°

We know that in a parallelogram adjacent angles are supplementary, so :

<x + 75° = 180°

<x = 180° - 75°

<x = 105°

We know that in a parallelogram opposite angles are equal, so :

<x = <z

<z = 105°

$\Large \mathfrak \orange {✽ \: Verification \:✽ }$

We know that sum of all the angles in a quadrilateral is 180°, so :

75° + <x + <y + <z = 360°

75° + 105° + 75° + 105° = 360°

360° = 360°

❄️ LHS = RHS

❄️ Henceforth, verified !!

$\Large \mathfrak \orange {✽ \: Conclusion \: ✽}$

Therefore,

• <x = 105°
• <y = 75°
• <z = 105°

_________________________

All done :)