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Maths-

General

Easy

Question

In the given figure, if $P Q parallel to R S comma angle M X Q equals 135 to the power of ring operator end exponent$ and $angle M Y R equals 40 to the power of ring operator end exponent$ then the value of $angle X M Y$ is

$70^{\circ}$
$85^{\circ}$
$80^{\circ}$
$105^{\circ} .$

The correct answer is: $85 to the power of ring operator end exponent$

We were given with a diagram and asked to find the angle

Draw a line AB parallel to PQ, so AB∥PQ and PQ∥RS, so AB∥RS.
It is known that the sum of two interior angles on the same side is 180, therefore,
∠QXM+∠XMB=180
∠XMB=180−135
∠XMB=45
alternate interior angles are equal, so,
∠BMY=∠MYR
∠BMY=40
Now, ∠XMY=∠XMB+∠BMY
=45+40
=85

Hence 85^o is correct option

Related Questions to study

In figure, if $A B parallel to C D comma C D parallel to E F$ and y : z = 3 : 7, x = ?

Hence x=126 choice 4 is correct

In figure, if $A B parallel to C D comma C D parallel to E F$ and y : z = 3 : 7, x = ?

Hence x=126 choice 4 is correct

In figure, if $A B parallel to D E comma angle B A C equals 35 to the power of ring operator end exponent$ and $angle C D E equals 53 to the power of ring operator end exponent comma angle D C E$ = ?

Hence 92^o
is correct choice

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Hence 92^o
is correct choice

In figure, sides QP and RQ of $triangle P Q R$ are produced to points S and T respectively. If $angle S P R equals 135 to the power of ring operator end exponent$ and $angle P Q T equals 110 to the power of ring operator end exponent comma angle P R Q$ =?

Hence choice A is correct

In figure, sides QP and RQ of $triangle P Q R$ are produced to points S and T respectively. If $angle S P R equals 135 to the power of ring operator end exponent$ and $angle P Q T equals 110 to the power of ring operator end exponent comma angle P R Q$ =?

Hence choice A is correct

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