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?

$69$

$72$

$90$

$102$

$108$

Answer: B

Concepts:angle sum linear equation

Difficulty rating: 1020

Solution:

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 .

2011 AMC 10B Problem 7

Answer: B

Difficulty rating: 1020

Solution:

Problem 7 in Other Years