An obtuse angle is formed by two adjacent angles with measures ( x - 5 ) and (3x). If the resulting angle measure is 107, what is the angle measure of each of the two unknown angles? Round to the nearest whole number.

Question

28 and 79

20 and 87

23 and 84

32 and 75

Answer 1

To find the measures of the two unknown angles, we start by setting up the equation based on the information given.

The two adjacent angles are $x-5$ and $3x$. The sum of their measures is given as 107 degrees:

$$(x-5)+(3x)=107$$

Now, combine like terms:

$$x-5+3x=107$$ $$4x-5=107$$

Next, add 5 to both sides of the equation:

$$4x=107+5$$ $$4x=112$$

Now, divide both sides by 4 to solve for $x$:

$$x=\frac{112}{4}=28$$

Now that we have the value of $x$, we can find the measures of the two angles:

1. The first angle: $$x-5=28-5=23$$

2. The second angle: $$3x=3\times 28=84$$

Thus, the two angle measures are $23$ and $84$.

Now, let's check the options provided:

• 28 and 79
• 20 and 87
• 23 and 84
• 32 and 75

The correct answer is $\boxed{{\displaystyle 23}}$ and $\boxed{{\displaystyle 84}}$.