Solve.
-In a triangular cross-section of a lean-to for water fowl in an aviary, the second angle is 3 times as large as the first angle. The measure of the third angle is 10° greater than that of the first angle. How large are the angles?
A)34°, 102°, 44°
B)34°, 146°, 146°
C)84°, 49°, 44°
D)84°, 246°, 92°

Question

Quizplus · Accepted Answer

Let x be the measure of the first angle.
Then the measure of the second angle is 3x.
And the measure of the third angle is x+10.
The sum of the angles in a triangle is 180°, so we have:
x + 3x + (x+10) = 180
5x + 10 = 180
5x = 170
x = 34
Therefore, the first angle is 34°, the second angle is 3x34 = 102°, and the third angle is x+10 = 44°.
Thus, the best choice is A. Let x be the measure of the first angle. Then, the second angle is 3x and the third angle is x + 10.

Since the sum of the angles in a triangle is 180°, we can write an equation:

x + 3x + (x + 10) = 180

Simplifying the equation, we get:

5x + 10 = 180

5x = 170

x = 34

Therefore, the angles are:

First angle = x = 34°
Second angle = 3x = 102°
Third angle = x + 10 = 44°

So, the best choice is A.

Solve. -In a Triangular Cross-Section of a Lean-To for Water Fowl