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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 ​

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 class=

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akposevictor

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°

MrRoyal

Angles in a triangle may or may not be congruent.

[tex]\mathbf{\angle S}[/tex] is 38 degrees because [tex]\mathbf{\angle S}[/tex] is one of the base angles of an isosceles triangle.

From the question, we have:

[tex]\mathbf{\angle SRQ = 104^o}[/tex]

The sum of angles in a triangle is 180.

So, we have:

[tex]\mathbf{\angle SRQ + \angle S + \angle Q = 180}[/tex]

and

[tex]\mathbf{\angle S = \angle Q }[/tex] --- base angles of an isosceles triangle.

So, we have:

[tex]\mathbf{104 + \angle S + \angle S = 180}[/tex]

Subtract 104 from both sides

[tex]\mathbf{2\angle S = 76}[/tex]

Divide both sides by 2

[tex]\mathbf{\angle S = 38}[/tex]

Hence, [tex]\mathbf{\angle S}[/tex] is 38 degrees because [tex]\mathbf{\angle S}[/tex] is one of the base angles of an isosceles triangle.

Read more about isosceles triangles at:

https://brainly.com/question/21495359

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