Question

A (2) In right angled triangle PQR, hypotenuse PR = 10 and side PQ = 5, what is the a measure of angle R?
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Answer 1

Answer:

Angle R would be 45 degrees

Step-by-step explanation:

The angle that lies opposite to the hypotenuse (i.e Angle Q ) will be equal to 90 degrees, first of all I'm not even sure if PQR is a right angled triangle as the a^2 + b^2 = c^2 formula does not imply here as: 5^2 + x^2 = 10^2

25 + x = 100

x = 100- 25

x= 75

and 75 does not have a proper square root but let's assume that's not the case then we can extend RQ and form an exterior angle..

using the exterior angle property (exterior angle = sum of interior opposite angles which are angle PRQ and QPR = exterior angle

so to find the exterior angle we do 180 - 90 (angle Q)

which gives us 90 degrees, so, angle PQR + QPR = 90

and I have to assume that the triangle PQR is an isosceles right angle triangle (as the image below) so angle R will be equal to Angle P = 45 degrees.. this answer did not have to be so long just wanted to clear up the topic.