Question

Choose and EXPLAIN your answer

In the figure below, PQR is an equilateral triangle and DEFG is a rectangle.


What can we say about the measure of angle DXY?

A) It will always be 150 degree.

B) It will always be 135 degree.

C) It will always be 120degree .

D) Can't say without knowing the dimensions of rectangle DEFG

Answer 1

Answer:

from d figure we can say that , DXPR is a trapezium in which XPR=PRD = 60° and XDR = 90° , sum of angles of a trapezium is 360° ,so solving dis we can get angle DXY =150 °

Answer 2

Answer:

Option (A) is correct.

Given:

PQR is an equilateral triangle

DEFG is a rectangle.

To find:

measure of ∠DXY

Step-by-step explanation:

It is given that,

PQR is an equilateral triangle.

All the sides of equilateral triangle sides are equal.

All the angles of equilateral triangle are equal i.e. 60°

hence,

∠PQR = ∠PRQ = ∠QRP = 60°

and DEFG is a rectangle.

Opposite side are equal.

All the angles are right angle i.e. 90°

hence,

∠EDG = ∠DGF = ∠FEG = ∠FED = 90°

Now, consider ΔXQD.

∠XQD = 60° and ∠XDQ = 90°

∠XDQ + ∠XQD + ∠QXD = 180° { sum of angles of triangle is 180°)

⇒ 90 + 60 + ∠QXD = 180

⇒ ∠QXD  = 180 - 150

⇒ ∠QXD  = 30°

Now, consider line QY

∠QXD  + ∠DXY  = 180  {linear angle}

⇒ 30 + ∠DXY  = 180

⇒ ∠DXY  = 180 - 30

⇒ ∠DXY  = 150°

Therefore, ∠DXY will always be 150 degree.

Option (A) is correct.

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