Question

Find the measurement of the biggest and the smallest angles in the adjacent figure.

Answer 1

Answer:

We know that:

∠1+∠2+∠3+∠4=360°

2x+30+3x-70+5x-30+3x+40=360

Step 1: Simplify both sides of the equation.

2x+30+3x−70+3x+40+5x−30=360

(2x+3x+3x+5x)+(30−70+40−30)=360  (Combine Like Terms)

13x+(−30)=360

13x−30=360

Step 2: Add 30 to both sides.

13x−30+30=360+30

13x=390

Step 3: Divide both sides by 13.

13x ÷13 = 390 ÷13

x=30

Now, substitute the value in the biggest and smallest angle angles.

5x-30⇒5(30)-30⇒120°

3x-70⇒3(30)-70⇒20°

Thus, the smallest and biggest angles are 120° and 20° respectively.

HOPE THIS HELPS :D

Answer 2

Total angle=360°
a1+a2+a3+a4=360°
Thus,
5x-30+2x+30+3x-70+3x+40=360°
13x-30=360°
13x=390°
x=390/13
x=30

Now, finding all the angles,
a1=2x+30=2(30)+30= 90°
a2=3x-70=3(30)-70=20°
a3=3x+40=3(30)+40=120°
a4=5x-30=5(30)-30=120°

Therefore, the biggest angles are a3=a4=120°
And the smallest angle is a2=20°