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If the measures of the angles of a triangle are x° . . . .

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by M7MBA » Sat Dec 02, 2017 5:41 am
If the measures of the angles of a triangle are x°, (x + 10)° and (x - 40)°, what is the measure of the smallest of these angles?

(A) 10°
(B) 20°
(C) 30°
(D) 70°
(E) 80°

The OA is C.

Why is C the correct answer? I don't understand it. I need some help.
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by Brent@GMATPrepNow » Sat Dec 02, 2017 8:19 am
M7MBA wrote:If the measures of the angles of a triangle are x°, (x + 10)° and (x - 40)°, what is the measure of the smallest of these angles?

(A) 10°
(B) 20°
(C) 30°
(D) 70°
(E) 80°
The 3 angles in a triangle add to 180°
So, x + (x + 10)+ (x - 40) = 180
Simplify: 3x - 30 = 180
Solve, x = 70

What is the measure of the smallest of these angles?
The smallest angle is (x - 40)
Since x = 70, we can take x - 40 and replace x with 70 to get...
The smallest angle = 70 - 40 = 30
Answer: C

ASIDE: The 3 angles are x°, (x + 10)° and (x - 40)°
Replace x with 70 to get: 70°, (70 + 10)° and (70 - 40)°
Evaluate to see that the 3 angles are 70°, 80° and 30°

Cheers,
Brent
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by [email protected] » Sat Dec 02, 2017 12:05 pm
Hi M7MBA,

Brent's Algebraic approach is arguably the fastest way to find the value of X - but you have to be careful, since the question does NOT ask for the value of X (it asks for the smallest of the 3 angles in the triangle). Since the angles of the triangle are x°, (x + 10)° and (x - 40)°, we can 'reorganize' the information a bit and stay focused on the smallest angle from the start:

Smallest Angle = (X - 40) = Y
"Middle" Angle = X = Y + 40
Largest Angle = X + 10 = Y + 50

Now the 3 angles, in order from least to greatest, are (Y), (Y+40) and (Y+50). Thus....

3Y + 90 = 180
3Y = 90
Y = 30 and we have the value of the smallest angle in front of us.

Final Answer: C

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by Scott@TargetTestPrep » Sun Sep 29, 2019 6:20 pm
M7MBA wrote:If the measures of the angles of a triangle are x°, (x + 10)° and (x - 40)°, what is the measure of the smallest of these angles?

(A) 10°
(B) 20°
(C) 30°
(D) 70°
(E) 80°

The OA is C.

Why is C the correct answer? I don't understand it. I need some help.
We see that the smallest angle is (x - 40) degrees. We can create the following equation to solve for x:

x + x + 10 + x - 40 = 180

3x = 210

x = 70

Therefore, the smallest angle is 70 - 40 = 30 degrees.

Answer: C

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