Question

Find the angels x,y,z in the following parallelogram​

Answer 1

Answer:

AO = BO

∴ ∠z = ∠OBA = 50°

∠z = 50°

$\huge\boxed{\fcolorbox{black}{</strong><strong>yell</strong><strong>ow</strong><strong>}{</strong><strong>∠z = 50°</strong><strong>}}$

∠z + ∠AOB + ∠OBA = 180° (Angle sum property)

50° + ∠AOB + 50° = 180°

∠AOB + 100° = 180°

∠AOB = 180° – 100°

∠AOB = 80°

∠AOB = ∠x (vertically opposite angle)

∠x = 80°

$\huge\boxed{\fcolorbox{black}{</strong><strong>yell</strong><strong>ow</strong><strong>}{∠</strong><strong>x</strong><strong> = </strong><strong>8</strong><strong>0°}}$

∵∠DCA = ∠z = 50°(vertically opposite angle)

∠DCB = ∠y +∠DCA

90° = ∠y + 50°

∠y = 90° - 50°

∠y = 40°

$\huge\boxed{\fcolorbox{black}{</strong><strong>yell</strong><strong>ow</strong><strong>}</strong><strong>{∠</strong><strong>y</strong><strong> = </strong><strong>4</strong><strong>0°}}$

Step-by-step explanation:

hope it helps you