2011 AMC 10B Problem 7

Question

The sum of two angles of a triangle is

\frac{6}{5}

of a right angle, and one of these two angles is

30^{\circ}

larger than the other. What is the degree measure of the largest angle in the triangle?

69

72

90

102

108

Convert

\dfrac65

of a right angle to degrees

Compare the third angle with the two angles whose sum and difference are known

The two angles add to

\frac 65 \cdot 90 = 108.

This makes the other angle

180-108=72.

Then, if the larger of the two angles is

x

then the smaller of them is

x-30

so their sum is

2x-30=108,

making

x=69.

This means no angle is larger than

72,

making the largest equal to

72.

Thus, the correct answer is B .

Problem 7 in other years