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# Geometry

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In triangle PQR, angle P = angle Q + angle R + 30 degrees. Of all three exterior angles of triangle PQR, what is the least exterior angle, in degrees?

Nov 5, 2021

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I recommend looking up the question directly on google before coming here. Usually, there is an answer there. I found the answer on brainly in less than a minute:

The exterior angle to the vertex P, measuring 90°

Step-by-step explanation:

The sum of the internal angles of any triangle needs to be equal 180 degrees. So, we can write two equations:

mP = mQ + mR

mP + mQ + mR = 180°

Substituting (mQ + mR) by mP in the second equation, we have:

mP + mP = 180°

mP = 90°

this right angle is the bigger angle in the triangle, because the sum of all three angles needs to be 180°.

Each exterior angle is the supplementary angle of the respective internal angle, so the bigger the internal angle, the smaller the external angle.

So if the bigger internal angle is mP = 90°, the smaller exterior angle is 180 - 90 = 90°.