Sally drew a circle with the right triangle prq inscribed in it, as shown below: if the measure of arc qr is 40 degrees, what is the measure of angle pqr? a) 20 degrees b) 40 degrees c) 50 degrees d) 70 degrees

D) 70 degrees

Step-by-step explanation:

Here,

Right triangle PRQ inscribed in a circle,

Let O be the centre of the circle,

If the measure of arc QR is 40 degrees,

By the central angle theorem,

,

Now, by the given options it is clear that measure of angle PQR can not 90°,

Thus, m∠PRQ = 90°,

∵ The sum of all interior angles of a triangle is supplementary,

m∠PRQ + m∠QPR + m∠PQR = 180°,

90° + 20° + m∠PQR = 180°,

110° + m∠PQR = 180°,

m∠PQR = 70°,

Hence, OPTION D would be correct.

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

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step-by-step explanation:

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