Question

in figure 5,if AB//CD then find the value of x and y. ​

Answer 1

Step-by-step explanation:

$\bf{\underline{\underline\red{Given:-}}}$

• AB // CD

• ∠PRD = 127°

• ∠APQ = 90°

• ∠QPR = y

• ∠PQR = x

$\bf{\underline{\underline\blue{To\:Find:-}}}$

• The value of x and y.

$\bf{\underline{\underline\green{Solution:-}}}$

As we know that:-

Exterior angle = Sum of interior opposite angles.

In ∆ PQR , QR is extended up to D.

So:-

Exterior angle = ∠PRD

Sum of Opposite angle = ∠PQR + ∠QPR

→ ∠PRD = ∠PQR + ∠QPR

→ 127° = x + y

→ x + y = 127° ..........(i)

As AB // CD

→ ∠PBR + ∠DRP = 180° ( Interior allied angles)

→ ∠PBR + 127° = 180°

→ ∠PBR = 180° - 127°

→ ∠PBR = 53°

As the sum of angles on a straight line = 180°.

→ ∠APQ + y + ∠PBR = 180°

→ 90° + y + 53° = 180°

→ 143 + y = 180°

→ y = 180° - 143°

→ y = 37°

From equation (i)

→ x + y = 127°

→ x + 37° = 127°

→ x = 127° - 37°

→ x = 90°.

$\underline{\boxed{ \rm \purple{ \therefore \: x = 90 \degree \: \: and \: \: \: y = 37 \degree}}}$