Question

solve it please last last question ​

Answer 1

Given :-

Angle XYZ = 64

XY is produced to P

YQ bisects Angle XXP

Required :-

( I) XYZ

( II) Reflex Angle QYP

Solution :-

We have

Angle ZYP + Angle XYZ = 180 ( LINEAR PAIR)

Angle ZYP + 64 = 180

Angle ZYP = 180 - 64

Angle ZYP = 116

NOW,

YQ bisects Angle ZYP ( Given)

THEREFORE Angle 1 = Angle 2 = 1 \ 2 (116)

= 58 ( Cancellation by 2)

Angle XYQ = Angle XYZ + Angle 1

= 64 + 58

= 122

NOW ,

Angle QYP = Angle 2 = 58

So Reflex = Angle QYP = 360 - 58

= 302

Note :-

Figure in attachment

Answer 2

Answer:

XP is a straight line

So, XYZ +ZYP = 180°

Substituting the value of XYZ = 64° we get,

64° +ZYP = 180°

∴ ZYP = 116°

From the diagram, we know that

ZYP = ZYQ + QYP

As YQ bisects ZYP,

ZYQ = QYP

Or, ZYP = 2ZYQ

∴ ZYQ = QYP = 58°

Again, XYQ = XYZ + ZYQ

Substituting the value of XYZ = 64° and ZYQ = 58° we get.

XYQ = 64°+58°

Or, XYQ = 122°

Now, reflex QYP = 180°+XYQ

The value of XYQ = 122°.

So,

QYP = 180°+122°

∴ QYP = 302°