Question

Hey can anyone help with this question chapter : Rectilinear figures.
Answer only if you know.​

Answer 1

Step-by-step explanation:

Given:-

In a Parallelogram ABCD ,AP and AQ are perpendiculars from the vertex of obtuse angle A and angle x : angle y = 2:1.

To find:-

Find the all angles in the given Parallelogram

Solution:-

ABCD is a Parallelogram

AP and AQ are perpendiculars drawn from A

and angle x : angle y = 2:1

Let they be 2a° and a°

angle x = 2a°

angle y = a°

Now ,

In the quadrilateral APCQ ,

angle QAP = y

angle AQC = 90°

angle QCP = x

angle APC = 90°

We know that

The sum of all angles in a quadrilateral is 360°

angle QAP + angle AQC + angle QCP + angle APC

= 360°

=>y+90°+x+90° = 360°

=>x+y+180°= 360°

=>x+y = 360°-180°

=>x+y= 180°

=>2a°+a° = 180°

=>3a° = 180°

=>a° = 180°/3

=>a°=60°

=>2a°=2×60°=120°

Therefore , angle C = 120°

we know that

Opposite angles are equal in Parallelogram

angle C = angle A = 120°

we know that

The adjacent angles are supplementary in Parallelogram

=>angle B + angle C = 180°

=>angle B +120° = 180°

=>angle B = 180°-120°

=>angle B = 60°

Therefore angle B = 60°

The opposite angle of angle B is angle D = 60°

Answer:-

The angles of a Parallelogram ABCD are

angle A = 120°

angle B = 60°

angle C = 120°

angle D = 60°

Used formulae:-

• The sum of all angles in a quadrilateral is 360°
• Opposite angles are equal in Parallelogram
• The adjacent angles are supplementary in Parallelogram