Question

10 find the measure of each angle.
∠3 and ∠4 are complimentary angles.
$m∠3=(3x + 4)^{circ}$, and $m∠4=(10x - 5)^{circ}$.
find $m∠3$ and $m∠4$.
$m∠3 =$
$m∠4 =$

Explanation:

Step1: Define complementary angles sum

Complementary angles sum to $90^\circ$. So:
$$(3x+4) + (10x-5) = 90$$

Step2: Simplify and solve for $x$

Combine like terms and isolate $x$:
$$13x - 1 = 90$$
$$13x = 91$$
$$x = \frac{91}{13} = 7$$

Step3: Calculate $m\angle3$

Substitute $x=7$ into $\angle3$ expression:
$$m\angle3 = 3(7) + 4 = 21 + 4 = 25$$

Step4: Calculate $m\angle4$

Substitute $x=7$ into $\angle4$ expression:
$$m\angle4 = 10(7) - 5 = 70 - 5 = 65$$

Answer:

$m\angle3 = 25^\circ$
$m\angle4 = 65^\circ$