Question

In the figure, if PQ II RS, angle MXQ = 135º and
angle MYR = 40°, find angle XMY. ​

Answer 1

Answer:

85 degree

Step-by-step explanation:

angle MYR = angle YMC = 40

{ ALTERNATE ANGLE }

PXQ is forming a linear pair,

135 + angle PXM = 180

Angle PXM = 45

angle PXM = angle XMC = 45

{ ALTERNATE ANGLE }

Angle XMY = 40 + 45

=. 85 degree

Answer 2

The measure of ∠XMY = 85°

Given:

In given figure, PQ || RS

∠MXQ = 135° and ∠MYR = 40°

To find:

Find angle XMY

Solution:

Draw a straight line T along M,

where T will be parallel to the lines PQ and RS

MX and MY are two transversal lines on parallel lines PQ, T and RS, T respectively

[ we will use it for further calculations ]

From straight line PQ

⇒ ∠ PXM + ∠ MXQ = 180°  

⇒  ∠ PXM = 180° - 135°

⇒ ∠ PXM = 45°  

As we know MX is transversal which cuts the lines PQ, T

⇒ ∠ PXM = ∠XMT  [ ∵  both are Alternate interior angles ]

⇒  ∠XMT = 45°

MY is transversal which cuts the lines RS, T

⇒ ∠MYR = ∠YMT   [ ∵  both are Alternate interior angles ]

⇒ ∠YMT = 40°  

⇒ ∠XMY =  ∠XMT + ∠YMT  

⇒ ∠XMY =  45° + 40° = 85°

Therefore the measure of ∠XMY = 85°

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