Question

in the figure AB is parallel to QR,angleBAQ=142⁰and angleABP=100⁰ .find a)angle APB ,b) angle ZAQ and c)QRP
plz tell fast this question its urgent ​

Answer 1

Answer:

first find PAB angle

Let it be 'x'

QAB+x=180°(Linear equation)

142°+x=180°

x=180°-142°

x=38°

PAB+APB+PBA=180°(sum of all angles of triangle)

38°+APB+100°=180°

138°APB=180°

APB=180°-138°

APB=42° is answer

Answer 2

Given:-

• ∠BAQ = 142°
• ∠PBR = 120°
• AB || QR

To Find:-

a) ∠APB

b) ∠AQR

c) ∠QRP

Solution:-

In The adjoining figure we can see that,

BAP is a triangle and AQRB is a quadrilateral.

In the given figure,

∠BAQ + ∠BAP = 180° [Linear Pair]

= $\sf{142^\circ + \angle BAP = 180^\circ}$

= $\sf{\angle BAP = 180^\circ - 142^\circ}$

= $\sf{\angle BAP = 38^\circ}$

Now,

In ∆BAP,

∠BAP = 38°

∠PBA = 100°

According to Angle-Sum property of a triangle,

$\sf{\angle BAP + \angle PBA + \angle APB = 180^\circ}$

= $\sf{38^\circ + 100^\circ + \angle APB = 180^\circ}$

= $\sf{138^\circ + \angle APB = 180^\circ}$

= $\sf{\angle APB = 180^\circ - 138^\circ}$

= $\sf{\angle = 42^\circ}$

a) Therefore measure of ∠APB is 42°

Now,

Also from the figure,

$\sf{\angle ABP + \angle ABR = 180^\circ\:\:[Linear\:Pair]}$

= $\sf{ 100^\circ + \angle ABR = 180^\circ}$

= $\sf{\angle ABR = 180^\circ - 100^\circ}$

= $\sf{\angle ABR = 80^\circ}$

Now,

$\sf{\angle QRP = \angle ABP}$ [Corresponding Angles]

Therefore,

$\sf{\angle QRP = 100^\circ}$

c) So, the measure of ∠QRB is 100°

Now,

In quadrilateral ABRQ,

∠QRB = 100°

∠ABR = 80°

∠BAQ = 142°

According to angle-sum property of a quadrilateral,

$\sf{\angle QRB + \angle ABR + \angle BAQ + \angle AQR = 360^\circ}$

= $\sf{100^\circ + 80^circ + 142^\circ + \angle AQR = 360^\circ}$

= $\sf{322^\circ + \angle AQR = 360^\circ}$

= $\sf{\angle AQR = 360^\circ - 322^\circ}$

= $\sf{\angle AQR = 38^\circ}$

b) Therefore the measure of ∠AQR is 38°

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→ What is angle-sum property of a triangle?

✓ Angle-sum property of a triangle states that sum of all the angles of a triangle is always 180°

→ What is angle-sum property of a quadrilateral?

✓ Angle-sum property of a triangle states that sum of all the angles of a quadrilateral is always 360°

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