Question

In figure 9.6, if AB||CD, angle:APQ=60° and angle:PRD =125°, find x and y.

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Answer 1

Answer:

$x \: = \: 60^{\circ} \: and \: y \: = \: 77^{\circ}$

GIVEN :

• $\sf AB \parallel CD$

• $\sf \angle APQ = 60^{\circ}$

• $\sf \angle PRD = 137^{\circ}$

TO FIND :

The values of x and y.

SOLUTION :

From the given figure,

R is a point angle. So, $\angle R = 180^{\circ}$

→ $\angle QRP \: + \: \angle PRD \: = \: 180^{\circ}$

→ $\angle QRP \: = \: 180^{\circ} \: - \: 137^{\circ}$

→ $\angle QRP \: = \: 43^{\circ}$

In $\triangle PQR,$

→ $x \: + \: y \: + \: 43^{\circ} \: = \: 180^{\circ}$

→ $x \: + \: y \: = \: 180^{\circ} \: - \: 43^{\circ}$

→ $x \: + \: y \: = \: 137^{\circ}$

$\therefore AB \parallel CD, \angle APQ \: and \: \angle PQR \: are \: alternate \: angles.$

Now, $\angle APQ \: = \: \angle PQR$

$\therefore \sf {\boxed {x \: = \: 60^{\circ}}}$

→ $60 \: + \: y \: = \: 137^{\circ}$

→ $y \: = \: 137 \: - \: 60$

$\therefore \sf {\boxed {y \: = \: 77^{\circ}}}$

Answer 2

1. angle x is equal to 60 degree, by co interior angles.
2. next, bi linear pair, angle PRQ=55 DEGREE
3. NOW USING, ANGLES ON A STRAIGHT LINE.... ANGLE Y IS EQUAL TO 65 DEGREE

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