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

Answer:

∠S = 45°

Step-by-step 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

$3x+2x+3x=180\\8x=180\\x=\frac{180}{8}$

So, ∠S=2x

∠S=$2\cdot \frac{180}{8}$

∠S=45°

Answer 2

Answer:

m∠S= 45°

Step-by-step 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 = $\frac{180}{8}$

     ⇒       x = $\frac{45}{2}$

Hence, m∠S = $2\times\frac{45}{2}$

                     = 45°