Question

XOY is a straight line and OQ is perpendicular to XY at O and OP is the bisector of QOX. Show that 2(QOP)=YOP-XOP

Answer 1

Step-by-step explanation:

this helps you l hope you understand

Answer 2

Therefore 2 (∠QOP) = ∠YOP - ∠XOP has been proved.

Given:

XY is a straight line.

OQ is perpendicular to XY at 'O' and also OP is the bisector of QOX.

To Find:

Show that 2(QOP)=YOP-XOP.

Solution:

The given question can be answered as shown below.

Given that

XY is a straight line.

OQ is perpendicular to XY at 'O' and also OP is the bisector of QOX as shown in the figure.

As OQ is perpendicular to XY ⇒ ∠YOQ = ∠XOQ = 90°

As OP is bisector of QOX ⇒ ∠QOP = ∠XOP = 45°

Given question to be proved: 2(∠QOP) = ∠YOP - ∠XOP

LHS: 2 (∠QOP) = 2 × 45° = 90°

RHS: ∠YOP - ∠XOP    [ ∠YOP = ∠YOQ + ∠QOP = 90° + 45° = 135°

∠YOP - ∠XOP = 135° - 45° = 90°

⇒ LHS = RHS

Hence Proved

Therefore 2 (∠QOP) = ∠YOP - ∠XOP has been proved.

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