there are angles whose measures add to 180°. Their measures are:

m<a= 67°; m<b= (2x + 20)°, and m‹c= x°. What is the measure of <b 1 point)
A 31°
B 180°
C 82°
D 62°

1 answer

We know that the sum of the measures of angles in a triangle is always 180°. Therefore, we can set up the following equation:

m<a + m<b + m‹c = 180°

Since we know the measures of angles m<a and m‹c, we can substitute those values into the equation:

67° + (2x + 20)° + x° = 180°

Combining like terms:

3x + 87° = 180°

To solve for x, we subtract 87° from both sides:

3x = 180° - 87°
3x = 93°

Dividing both sides by 3:

x = 31°

Now that we have the value of x, we can substitute it back into the expression for the measure of angle b:

m<b = 2x + 20°
m<b = 2(31°) + 20°
m<b = 62° + 20°
m<b = 82°

Therefore, the measure of angle b is 82°. The answer is option C.