Two complementary angles have measures (4x)°

Question

and (2x)°
. What is the value of x
and the two angle measures?

Answer 1

Complementary angles are two angles that add up to 90 degrees. Given the two angles are $(4x{)}^{\circ }$ and $(2x{)}^{\circ }$, we can set up the following equation:

$$4x+2x=90$$

Combining like terms:

$$6x=90$$

Now, we can solve for $x$ by dividing both sides by 6:

$$x=\frac{90}{6}=15$$

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

1. The first angle: $$4x=4(15)={60}^{\circ }$$

2. The second angle: $$2x=2(15)={30}^{\circ }$$

Thus, the value of $x$ is $15$, and the measures of the two angles are ${60}^{\circ }$ and ${30}^{\circ }$.