Question

Answer The Following

Answer 1

Angle B = 110

Angle S = 60

Longest angle = B

Shortest angle = T

Longest side = TS

Shortest side -= BS

Explanation:

Sum of total angles of an triangle = 180

So angle (B +S + T ) = 180

(2x + 50) + 10 + (x + 30) = 180

3x = 90

x = 30

So angle B = 110, S = 60, T = 10

Longest side of a triangle is the side opposite to obtuse angle (B) which is TS

Answer 2

m∡B=110°

m∡S =60°

Largest Angle =m∡B

Shortest Angle= m∡T

largest side: ST

Shortest side: BS

Explanation:

Solution Given:

First of all, let's find the value of x.

Since the sum of interior angle of a triangle is 180°.

m∡B + m∡S + m∡T=180°

2x+50°+x+30°+10°=180°

Adding like terms

2x+x+30°+10°+50°=180°

3x+90°=180°

subtracting both side by 90°

3x=180°-90°

3x=90°

Dividing both side by 3.

x=90°/3=30°

Now,

m∡B=2x+50°=2*30+50°=110°

m∡S=x+30°=30°+30°=60°

Since, m∡B > m∡S > m∡T

So,

Largest Angle =m∡B

Shortest Angle= m∡T

Again,

Since, the opposite side of largest angle has largest side and the opposite side of shortest angle has shortest side.

Therefore,

largest side: ST

Shortest side: BS