Question

One angle of a triangle measures 16∘ more than the smallest, while a third angle is twice the smallest. Find the measure of each angle.

Answer 1

Answer:

Smallest angle: 41°

Second angle: 57°

Third angle: 82°

Step-by-step explanation:

Let's call the smallest angle as $x$

"while a third angle is twice the smallest": third angle is $2x$

"One angle of a triangle measures 16∘ more than the smallest": 2nd angle is $16+x$

We know sum of 3 angles in a triangle is 180 degrees, so we can set up the equation and solve for x:

$x+(16+x)+(2x)=180\\x+16+x+2x=180\\4x=180-16\\4x=164\\x=\frac{164}{4}=41$

So smallest angle is 41°

The 2nd angle is 16+41=57°

third angle is 2*41=82°

Answer 2

Answer:

• The smallest angle is 41
• The second angle is 57
• The third angle is 2*41 = 82

Step-by-step explanation:

Givens

• Let the smallest angle = x
• The second angle is x + 16
• The third angle is 2x
• The total is 180o because all triangles have 180 degrees.

Solution

• x + x + 16 + 2x = 180
• 4x + 16 = 180                Subtract 16
• 4x = 180 - 16
• 4x = 164                         Divide both sides by 4
• 4x/4 = 164/4
• x = 41