Question

It is given that angle XYZ=64 degree and XY is produced to point P. Draw a figure from the given information. If ray YQ bisects angle ZYP , find angle XYQ and reflex angle QYP.​

Answer 1

${\huge{\underline{\underline{\bold{\red{Answer:-}}}}}}$

$⇒$It is given that line YQ bisects ∠PYZ.

${\huge{\underline{\small{\bold{\green{Hence,}}}}}}$

$⇒$∠QYP = ∠ZYQ

$⇒$PX is straight line

$⇒$sum of angle in linear pair always equal to 180°

$⇒$∠XYZ + ∠ZYQ + ∠QYP = 180°

$⇒$Give that so plug the value we get ∠ XYZ = 64° And ∠QYP = ∠ZYQ

$⇒$∠ 64° + 2∠QYP = 180°

$⇒$∠2∠QYP = 180° − 64° = 116°

☁Divide by 2 we get

$⇒$∠QYP = 58°

${\huge{\underline{\small{\bold{\blue{Also,}}}}}}$

$⇒$∠ZYQ = ∠QYP = 58°

☁Using angle of reflection

$⇒$∠QYP = 360° − 58° = 302°

$⇒$∠XYQ = ∠XYZ + ∠ZYQ

$⇒$64° + 58°

$⇒$122°

${\huge{\underline{\small{\bold{\purple{hope\:help\:u :)}}}}}}$

Answer 2

Question :-

It is given that ∠XYZ = 64° and XY is produced to point P. Draw a figure from the given information. If ray YQ bisects ∠ZYP, find ∠XYQ and reflex ∠QYP.

Answer :-

ie : XYP is a straight line.

∴ ∠XYZ + ∠ZYQ + ∠QYP = 180°

⇒ 64° + ∠ZYQ + ∠QYP = 180°

[∵ ∠XYZ = 64° (given)]

⇒ 64° + 2∠QYP = 180°

[YQ bisects ∠ZYP so, ∠QYP = ∠ZYQ]

⇒ 2∠QYP = 180° – 64° = 116°

⇒ ∠QYP = 116°/2 = 58°

∴ Reflex ∠QYP = 360° – 58° = 302°

Since ∠XYQ = ∠XYZ + ∠ZYQ

⇒ ∠XYQ = 64° + ∠QYP [∵∠XYZ = 64°(Given) and ∠ZYQ = ∠QYP]

⇒ ∠XYQ = 64° + 58° = 122° [∠QYP = 58°]

Thus, ∠XYQ = 122° and reflex ∠QYP = 302°.

Plz mrk as brainliest ❤