Difference between revisions of "2021 JMPSC Sprint Problems/Problem 3"

(Problem)
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==Solution==
 
==Solution==
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It is given that the right angles are <math>90</math> degrees, and that all the angles in the two triangles are all equal. We can already infer that the black angles are all <math>60</math> degrees, since they are equilateral triangles.
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There are <math>360</math> degrees in a whole circle. We are given two of the black curves, and a <math>90</math> degree angle, in which all three of them add up to <math>210</math> degrees.
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<math>360-210=150</math>. Therefore, the angle marked with a question mark has a measure of <math>150</math> degrees.

Revision as of 00:50, 11 July 2021

Problem

If all angles marked with a red square are $90^\circ$ and all angles marked with one black curve are equal, find the measure of the angle with a question mark.

Sprint4.png

Solution

It is given that the right angles are $90$ degrees, and that all the angles in the two triangles are all equal. We can already infer that the black angles are all $60$ degrees, since they are equilateral triangles.

There are $360$ degrees in a whole circle. We are given two of the black curves, and a $90$ degree angle, in which all three of them add up to $210$ degrees.

$360-210=150$. Therefore, the angle marked with a question mark has a measure of $150$ degrees.