Question

in the given figure,if AB=7.5cm,BC=5cm and CA=6.3cm,then x,y,z arranged in ascending order.​

Answer 1

Given:

AB = 7.5cm

BC = 5cm

CA = 6.3cm

To find:

Arrange the angles x, y and z in ascending order.

Solution:

We know that, in a triangle, the angle opposite to the longer side will be the largest angle.

So, the angle opposite to AB = 7.5cm, that is ∠C, is the largest angle.

Angle opposite to CA = 6.3cm, that is ∠B, is the second largest.

Angle opposite to BC = 5cm, that is ∠A, is the smallest.

Now, AB, BC and CA are straight lines.

So, $x=$ 180°-∠A

$y=$180°-∠B

$z=$180°-∠C

Thus,

$z$ will be the smallest since when we subtract the largest measure from 180° it produces a smaller angle compared to when we subtract the smaller angle from 180°.

So, $x$ will be the largest angle.

Hence the angles x,y and z in ascending order is $x>y>z$.

Answer 2

Ascending order will be z , y , x  where ∠x , ∠y  and ∠z are exterior of ∠A , ∠B and ∠C respectively in ΔABC where AB=7.5cm,BC=5cm and CA=6.3cm

Given :

• ΔABC
• AB = 7.5 cm
• BC = 5 cm
• CA= 6.3 cm
• ∠x is exterior of ∠A
• ∠y is exterior of ∠B
• ∠z is exterior of ∠C

To Find:

• x,y,z to be arranged in ascending order.​

Solution:

"Triangle Angle-Side Relationship Theorem"

Sides opposite to larger angle is longer or vice-versa

" Linear pair adds up to 180°"

Step 1:

Arrange sides in order

7.5 > 6.3 > 5

AB > CA > BC

Step 2:

Arrange angles in order as per side length

∠C  > ∠ B > ∠A

Step 3:

Multiply with -1   ( on multiplication with negative , inequality signs changes)

-∠C < -∠ B < -∠A

Step 4:

Add 180° Each side

180° -∠C < 180°-∠ B <180°-∠A

Step 5:

Using linear pair relationship:

180° -∠C = ∠z

180°-∠ B =∠y

180°-∠A = ∠x

z° <  y°  < x°

x,y,z arranged in ascending order will be z , y , x

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