The measure of the largest angle in a triangle is 50◦ larger than the sum of the measures of the other two angles.

Question

The measure of the largest angle in a triangle is 50◦ larger than the sum of the measures of the other two angles. The measure of the smallest angle is half the measure of the middle angle Find the measure of each angle.

Answer 1

Let's let m∠ L = the measure of largest angle

m∠ M = the measure of middle angle

m∠ S= the measure of smallest angle

L = M + S + 50 -----> L = M +(M ÷ 2) + 50

L + M + S = 180

S = M ÷ 2

So, we can substitute these two expressions in for L & S in order to solve for m∠ M.

L + M + S = 180

[M + (M ÷ 2) + 50] + M + (M ÷ 2) = 180

[2M/2 + M/2 + 100/2] + M + M/2 = 180

(3M + 100)/2 + M + M/2 = 180

3M + 100 + 2M + M

¯¯¯¯¯¯¯¯¯2¯¯¯¯¯¯ --------- > (6M + 100)/2 = 180 -------> 3M + 50 = 180

-50 -50

3M = 130

÷3 ÷3

M = 43.33333 degrees

3(43 1⁄3) + 50 = 180

130 + 50 = 180

43 1⁄3 + 115 + 21 2⁄3 = 180?

L = 43 1⁄3 + (43 1⁄3 ÷ 2) + 50 65 + 115 = 180

L = 43 1⁄3 + (43 1⁄3 × 1⁄2) + 50

L = 130⁄3 + 130⁄3 ×1⁄2 + 50

L = 130⁄3 + 130⁄6 + 50

L = 260⁄6 + 130⁄6 + 300⁄6 = 690⁄6 = 115 degrees

S = 43 1⁄3 ÷ 2 = 130⁄6 or 21 4⁄6 = 21 2⁄3 degrees

Answer 2

L=50+ M+ S

S= (1/2)M

L+M+S = 180

3 equations 3 unknowns

50 + M + M/2 + M + M/2 = 180

3M = 130

M = 130/3 = 43 1/3 degrees

S = M/2 = 21 2/3 degrees

L = 50 + 43 1 + 21 2/3 = 115 degrees