In the diagram shown, it is known that RP is perpendicular to QS and RP bisects angle SRQ. If angle SRQ is 104 degrees, then explain why angle S is 38 degrees. pls help

Angles in a triangle may or may not be congruent.

is 38 degrees because is one of the base angles of an isosceles triangle.

From the question, we have:

The sum of angles in a triangle is 180.

So, we have:

and

--- base angles of an isosceles triangle.

So, we have:

Subtract 104 from both sides

Divide both sides by 2

Hence, is 38 degrees because is one of the base angles of an isosceles triangle.

Read more about isosceles triangles at:

link

Answer/Step-by-step explanation:

Since RP is perpendicular to QS, the angle formed is a right angle, therefore,

m<SPR = 90°

Since RP bisects <SRQ, which measures 104°, therefore,

m<SRP = ½*104°

m<SRP = 52°

m<S + m<SPR + m<SRP = 180° (sum of ∆)

m<S + 90° + 52° = 180° (substitution)

m<S + 142° = 180°

Subtract 142 from each side

m<S = 180° - 142°

Therefore:

m<S = 38°