Difference between revisions of "1999 CEMC Gauss (Grade 7) Problems/Problem 6"
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==Problem== | ==Problem== | ||
In <math>\Delta ABC</math>, <math>\angle B = 72^{\circ}</math>. What is the sum, in degrees, of the other two angles? | In <math>\Delta ABC</math>, <math>\angle B = 72^{\circ}</math>. What is the sum, in degrees, of the other two angles? | ||
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<math>\text{(A)}\ 144 \qquad \text{(B)}\ 72 \qquad \text{(C)}\ 108 \qquad \text{(D)}\ 110 \qquad \text{(E)}\ 288 </math> | <math>\text{(A)}\ 144 \qquad \text{(B)}\ 72 \qquad \text{(C)}\ 108 \qquad \text{(D)}\ 110 \qquad \text{(E)}\ 288 </math> | ||
==Solution== | ==Solution== | ||
Latest revision as of 12:31, 22 April 2025
Problem
In 
, 
. What is the sum, in degrees, of the other two angles?
An image is supposed to go here. You can help us out by creating one and editing it in. Thanks.
Solution
Let x and y be the other two angles of the triangle.
The sum of the interior angles in a triangle is always 
, so we have:
Subtracting 
from both sides of the equation gives:
