SOLUTION: If the measures of the angles of a triangle are in the ratio 1:3:5, the number of degrees in the measure of the smallest angle is

Question 243712: If the measures of the angles of a triangle are in the ratio 1:3:5, the number of degrees in the measure of the smallest angle is
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
This problem hinges on your remembering that the sum of the angles in a triangle is always 180.
.
In this case we have 3 unknown angles: a, b, and c.
However, we are told they have a specific relationship: 1 to 3 to 5. So the second angle is 3 times the first and the third angle is 5 times the first.
.
a = a
b = 3a
c = 5a
.
a + b + c = 180
Substituting,
a + 3a + 5a = 180
9a = 180
Divide both sides by 9
a = 20
.
Substituting back into the formulas we defined.
a = 20
b = 3a = 3(20) = 60
c = 5a = 5(20) = 100
.
Check the work.
Does 20 + 60 + 100 = 180?
Yes.
.
Done.
RELATED QUESTIONS
If the measures of the angles of a triangle are in the ratio 1:3:5, the number of degrees (answered by solver91311)

the measure of the angles of a triangle are in the ratio 1:3:5 the smallest angle in... (answered by Alan3354)

the measure of the angles of a triangle are in the ratio 1:2:3. what is the measure(in... (answered by solver91311)

if the measure of the angles of a triangle are in the ratio 2:3:4, the measure of the... (answered by user_dude2008)

Can you help me with this problem please? "If the measures of the angles of a triangle... (answered by stanbon)

The measures of the two acute angles in a right triangle are in the ratio 2:3. What is... (answered by edjones,richwmiller)

if 2 angles are complementary , find the measure of the smallest angle of the measures of (answered by 2897696,jim_thompson5910)

The measures of the angles of a triangle are in the extended ratio 4 : 5 : 6. What is the (answered by Fombitz)

The measures of two complementary angles are in a ratio of 7:5 Find the Measure of the... (answered by checkley71)