Together, the measures of LB, LC, and LD equal 180°. The angles have the following measures: m<B = 25°, mLC = (3x) °
, and mLD = (3x + 5)*. What are the
measures of LC and LD?
Given that LB, LC, and LD measure 25°, 3x°, and (3x + 5)° respectively, and that they add up to 180°, we can write the equation:
25 + 3x + 3x + 5 = 180
Combining like terms:
25 + 6x + 5 = 180
30 + 6x = 180
Subtracting 30 from both sides:
6x = 150
Dividing by 6:
x = 25
Now we can find the measures of LC and LD:
LC = 3x = 3(25) = 75°
LD = 3x + 5 = 3(25) + 5 = 75 + 5 = 80°
Therefore, the measure of LC is 75° and the measure of LD is 80°.