Question

The angles of a triangle are such that one angle is 130 more than the smallest angle, while the third angle is 3 times as large as the smallest angle. Find the measures of all three angles

Answer 1

Answer:

$One\ angle: 140^o\\Smallest\ angle: 10^o\\Third\ angle: 30^o$

Step-by-step explanation:

Let

x ----> the measure of one angle of the triangle

y ---> the measure of the smallest angle

z ----> the measure of the third angle

we know that

The sum of the measure of the interior angles in any triangle must be equal to 180 degrees

$x+y+z=180^o$ -----> equation A

one angle is 130 degrees more than the smallest angle

$x=y+130$ ----> equation B

the third angle is 3 times as large as the smallest angle

$z=3y$ ---> equation C

substitute equation B and equation C in equation A

$(y+130)+y+3y=180^o$

solve for y

$5y=180-130\\5y=50\\y=10^o$

Find the value of x

$x=10+130=140^o$

Find the value of z

$z=3(10)=30^o$

therefore

$One\ angle: 140^o\\Smallest\ angle: 10^o\\Third\ angle: 30^o$