Question

5.
According to the diagram, the value of (a + b) in degrees is​

Answer 1

Answer:

The answer is obtained using the property:

The sum of two interior angles is equal to the measure of the opposite exterior angle--------hope you remember

Step-by-step explanation:

1. in QAM,

∠a + ∠QAM = ∠RMN [1]

2. in ΔNMR,

∠b + ∠RMN = 125

∠RMN = 125 - b [2]

3. Using [1] and [2]

125 - b = a + 55  [55 = ∠QAM]

a + b = 125 - 55

a + b = 70

Answer 2

In  $\bigtriangleup$ $AQM$

Sum angles =$180$°

$\angle AQM + \angle QAM + \angle AMQ =$ $180$°

⇒ $\angle AMQ =$ $125$° $- \alpha$

Now , $\angle AMQ + \angle RMN =$ $180$° ( Linear Pair)

$125$° $- \alpha$$+ \angle RMN =$ $180$°

⇒ $\angle RMN =$  $55$° $+ \alpha$

Also, $\angle PRM + \angle MRN =$  $180$°  ( Linear Pair)

⇒$125$°  $+ \angle MRN =$   $180$°

⇒ $\angle MRN = 55$°

Now, in Δ $MRN$

Sum of angles  $= 180$°

$\angle MRN = \angle RMN + \angle RNM = 180$°

⇒ $55$° $+ 55$° $+$ $\alpha$° $+$ $\beta$° $= 180$°

⇒  $\alpha + \beta$  $= 70$°

Hence , value of $\alpha + \beta$  is $70$ °

WHAT IS DEGREE ?

A degree is a unit used to represent the measurement of an angle. While measuring any angle we use the degrees symbol to denote it. It is denoted by °.

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