In triangle ABC the measure of angle A is four times that of angle B In addition the measure of angle C is 15 degrees than half the measure of angle A?

Answer 1

This doesn't ask any question but I assume you want to know the measures of angles ABC.

Well if C is 15 degrees LESS than half of angle A then the algebraic equation would look something like this:

Let x = measure of angle B then 4x = measure of angle A, since angle A is four times angle B

then 2x (half the measure of angle A = 4/2) - 15 = measure of C.

Basic Knowledge:

angle A+ angle B+ angle C=180°

180 degrees = total measure of angles in a triangle

4x° + x° + (2x - 15)° = 180°

SOLVE for X!

STEP 1: always combine (add/subtract) like terms

7x°-15+15=180°+15(isolate the variable by adding 15 on both sides of the equation)

_________

7x°/7+0 = 195°/7 (solve for x by dividing 7 on both sides of the equation)

_________

x ≃ 27.86° or = (27 6/7)° = measure of angle B

4x ≃ 111.44° = measure of angle A

2x-15 ≃ 55.72°-15 ≃ 40.72° = measure of angle C

**add them all up together, they would add up to 180.02° because x actually equals 27.857142857142857142.....

Now if C is 15 degrees MORE than half of angle A then the algebraic equation would look something like this:

again; Let x° = measure of angle B

then 4x° = measure of angle A, since angle A is four times angle B

then 2x (half the measure of angle A = 4/2) +15 = measure of C.

4x° + x° + (2x + 15)° = 180°

SOLVE for X! (same steps, just watch for the signs)

7x°+15-15=180° -15 (subtracted 15 on both sides)

_________

7x°/7 +0 = 165°/7 (divided 7 on both sides)

_________

x ≃ 23.57° or = (23 4/7)° = measure of angle B

4x ≃ 94.28° = measure of angle A

2x+15 ≃ 47.14° +15 ≃ 62.14° = measure of angle C

**add them all up together, they would add up to 179.99° because x actually equals 23.571428571428571428.....

See the pattern?? and the difference??