Question

an angle measures $46^\circ$ more than the measure of its supplementary angle. what is the measure of each angle?
$\boldsymbol{\square}^\circ$ and $\boldsymbol{\square}^\circ$

Explanation:

Step1: Define variables for angles

Let the smaller angle be $x$. The larger angle is $x + 46^\circ$.

Step2: Use supplementary angle property

Supplementary angles sum to $180^\circ$.
$$x + (x + 46^\circ) = 180^\circ$$

Step3: Simplify and solve for $x$

$$2x + 46^\circ = 180^\circ$$
$$2x = 180^\circ - 46^\circ = 134^\circ$$
$$x = \frac{134^\circ}{2} = 67^\circ$$

Step4: Find the larger angle

$$x + 46^\circ = 67^\circ + 46^\circ = 113^\circ$$

Answer:

$67^\circ$ and $113^\circ$