A) There are angles whose measures add to 180°. Their measures are: m LA = 67°, m<B= (2x + 20)°
, and m LC'= x". What is the measure of LB?
The sum of angle measures in a triangle is always 180°. Therefore, we can write the equation:
mLA + m<B + mLC' = 180
Substituting the given values, we have:
67 + (2x + 20) + x = 180
Combining like terms:
3x + 87 = 180
Subtracting 87 from both sides:
3x = 93
Dividing both sides by 3:
x = 31
Now we can find the measure of LB by substituting the value of x back into the equation:
mLB = 2x + 20
mLB = 2(31) + 20
mLB = 62 + 20
mLB = 82
Therefore, the measure of LB is 82°.