Question

tionships study guide
points: 0 of 1
part 1 of 3
challenge the angles shown are complementary angles. the measure of ∠1 is $(17x - 25)^{circ}$ and the measure of ∠2 is $(3x - 5)^{circ}$. find the value of x. then find the measures of ∠1 and ∠2. the figure is not drawn to scale.
the value of x is □

Explanation:

Step1: Set up complementary angle equation

Complementary angles sum to $90^\circ$, so:
$$(17x - 25) + (3x - 5) = 90$$

Step2: Simplify the left side

Combine like terms:
$$20x - 30 = 90$$

Step3: Isolate the term with x

Add 30 to both sides:
$$20x = 120$$

Step4: Solve for x

Divide both sides by 20:
$$x = \frac{120}{20} = 6$$

Step5: Calculate $m\angle1$

Substitute $x=6$ into $\angle1$'s expression:
$$m\angle1 = 17(6) - 25 = 102 - 25 = 77$$

Step6: Calculate $m\angle2$

Substitute $x=6$ into $\angle2$'s expression:
$$m\angle2 = 3(6) - 5 = 18 - 5 = 13$$

Answer:

The value of $x$ is $6$.
The measure of $\angle1$ is $77^\circ$.
The measure of $\angle2$ is $13^\circ$.