Question

apply: finding unknown angle measures
two angles, ∠1 and ∠2, are complementary angles. the measure of ∠2 is 32° less than the measure of ∠1.
what are the measures of the angles?
click or tap the correct measure from each drop - down menu.
the measure of ∠1 is choose
the measure of ∠2 is choose

Explanation:

Step1: Define variables

Let the measure of $\angle 1$ be $x$ degrees. Then the measure of $\angle 2$ is $x - 32$ degrees (since $\angle 2$ is $32^\circ$ less than $\angle 1$).

Step2: Use complementary angles property

Complementary angles add up to $90^\circ$. So we set up the equation:
$$x + (x - 32) = 90$$

Step3: Solve the equation

Simplify the left side:
$$2x - 32 = 90$$
Add 32 to both sides:
$$2x = 90 + 32$$
$$2x = 122$$
Divide both sides by 2:
$$x = \frac{122}{2}$$
$$x = 61$$

Step4: Find measure of $\angle 2$

Substitute $x = 61$ into the expression for $\angle 2$:
$\angle 2 = 61 - 32 = 29$ degrees.

Answer:

The measure of $\angle 1$ is $61^\circ$, and the measure of $\angle 2$ is $29^\circ$.