Question

What is m∠S?

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__°

An isosceles triangle with vertices labeled R, S, and T. Side R T is the base. Sides R S and side S T are equal. Angle R is labeled as 3 x degrees, angle S is labeled as 2 x degrees, and angle T is labeled as 3 x degrees.

Answer 1

m∠S= 45°

Explanation:

Given an isosceles triangle ABC.

& m∠R = m∠T = 3 x, m∠S = 2 x

The sum of all the angles of triangle is equal to 180°

⇒ m∠R + m∠S + m∠T = 180°

3 x + 2 x + 3 x = 180°

⇒ 8 x = 180°

⇒ x =
`(180)/(8)`

⇒ x =
`(45)/(2)`

Hence, m∠S =
`2*(45)/(2)`

= 45°

Answer 2

∠S = 45°

Explanation:

As given in the question, ∠R = 3x ; ∠S=2x ; ∠T=3x

So by using angle sum property of a triangle that sum of all the angles of a triangle is 180°.

We get, ∠R+∠S+∠T = 180

`3x+2x+3x=180\\8x=180\\x=(180)/(8)`

So, ∠S=2x

∠S=
`2\cdot (180)/(8)`

∠S=45°