Question

The measure of one angle is 13 less than five times The measure of another angle. The sum of the measure of the two angles is 140°. Determine the angle of each measure in degrees

Answer 1

$\huge\boxed{a=\frac{229}{2};\ \ b=\frac{51}{2}}$

In decimal form, a = 114.5; b = 25.5

We will write this as a system of equations, where $a$ and $b$ are the two angles.

$\left \{ {{a=5b-13} \atop {a+b=140}} \right$

We will use substitution to solve this system. We know what $a$ equals, so we plug that into the second equation.

$5b-13+b=140$

Combine the like terms.

$6b-13=140$

Add $13$ on both sides.

$6b=153$

Divide both sides by $6$.

$b=\frac{153}{6}=\boxed{\frac{51}{2}}$

Now just subtract that from $140$.

$a=140-\frac{51}{2}=\boxed{\frac{229}{2}}$