Question

a triangular playground has angles with measures in the ratio 8 : 5 : 2. what is the measure of the smallest angle?

Answer 1

>>> 24°

Explanation:

Given that ,

• Angle of triangular playground are in ratio that is 8 : 5 : 2

We have to find ,

• Measure of Smallest angle

Solution :

Let us say Angles of triangle are :

• 8x , 5x and 2x

For finding the measure of angles of triangle we are using Interior Angle Property of triangle which states that sum of all the three interior angles of triangle is equal to 180°.

`\dashrightarrow \: \: \sf{8x + 5x + 2x = 180}`

Simplifying LHS by adding them :

`\dashrightarrow \: \: \sf{15x = 180}`

Dividing both sides with 15 :

`\dashrightarrow \: \: \sf{ \frac{ \cancel{15}x}{ \cancel{15}} = \cancel{ (180)/(15)}}`

We get ,

`\dashrightarrow \: \: \underline{ \boxed{ \sf{ \bold{x = 12 {}^( \circ) }}}} \: \: \: \bigstar`

Now , Angles of triangle are :

• 1) 8x

→ 8 × 12

→ 96°

• 2) 5x

→ 5 × 12

→ 60°

• 3) 2x

→ 2 × 12

→ 2 × 12

→ 24° ★

From above we can see that smallest angle is 24°. Therefore , smallest angle of triangular playground is "24°" :)