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

*attachment contains the missing diagram

Answer/Step-by-step explanation:

Given that RP ⟂ QS, <RPS is a right angle.

Therefore, m<RPS = 90°

Since RP bisects <SRQ, therefore m<PRS = ½ of m<SRQ.

Therefore:

m<PRS = ½*104°

m<PRS = 52°

m<S + m<RPS + m<PRS = 180° (sum of ∆)

m<S + 90° + 52° = 180° (substitution)

m<S + 142 = 180°

Subtract 142 from each side

m<S = 180° - 142°

m<S = 38°

multiply then divide

step-by-step explanation:

isocolese triangle

we know that the line connect a and b is the hyptonuse

so first find the hypotonuse length using the distance formula, call the length c

since it is an isocolese triangle, the lengths of the legs are the same

using pythagorean theorem,

in this case, a=b since isocolese triangle so we get

or

we can find c so we can find the distances

we know that if we draw 2 circles, each has center at a and b, and find where they intersect, we can the 2 possible locations for c

if a has center at (xa,ya) and b has center at (xb,yb), then we can solve where

and

intersect to find where they intersect

i'm not going to put an example because i have to go to class. i hope this explanation is enough