Answer:
m<PRQ=15°
Step-by-step explanation:
so we're given that PQ and RQ are sides of a regular 12-sided polygon (dodecagon)
a regular polygon is a polygon that has all angles be the same measure AND have all sides be the same length
because of that, PQ=RQ, and ΔPQR is isoceles
now we need to find what the question is asking for: m<PRQ
because of base-angles theorem, m<PRQ=m<RPQ
we need to find m<PQR
a dodecagon is 1800° in measure
and we need 1/12th of that measure, since <PQR is 1 out of the 12 interior angles on the dodecagon (a dodecagon has 12 vertecies, so 12 angles). Also because the polygon is regular, every interior angle has the same measure.
so find the measure of <PQR
<PQR= 1/12*1800=150°
now to find the measure of <PRQ:
there are 180° in a triangle
so subtract 150° from 180°
180°-150°=30°
30° is the sum of the base angles (<PRQ is one of the base angles in a triangle)
the base angles are the same measure, so that means the measure of <PRQ is 1/2 the measure of the sum of the base angles
therefore m<PRQ=15°
hope this helps!
