Difference between revisions of "2011 AMC 10B Problems/Problem 7"
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− | The sum of two angles in a triangle is <math>\frac{6}{5}</math> of a right angle <math>\longrightarrow \frac{6}{5} \times | + | The sum of two angles in a triangle is <math>\frac{6}{5}</math> of a right angle <math>\longrightarrow \frac{6}{5} \times 90 = 108</math> |
If <math>x</math> is the measure of the first angle, then the measure of the second angle is <math>x+30</math>. | If <math>x</math> is the measure of the first angle, then the measure of the second angle is <math>x+30</math>. |
Revision as of 14:10, 13 November 2011
Problem
The sum of two angles of a triangle is of a right angle, and one of these two angles is larger than the other. What is the degree measure of the largest angle in the triangle?
Solution
The sum of two angles in a triangle is of a right angle
If is the measure of the first angle, then the measure of the second angle is .
Now we know the measure of two angles are and . By the Triangle Sum Theorem, the sum of all angles in a triangle is so the final angle is . Therefore, the largest angle in the triangle is
See Also
2011 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |