Question

∠7=(2x + 25)°, ∠8=(4x - 5)°. identify the angle relationship. solve for x. find ∠7 and ∠8.

Explanation:

Step1: Assume supplementary angles

Assume $\angle7$ and $\angle8$ are supplementary, so $\angle7+\angle8 = 180^{\circ}$.
$$(2x + 25)+(4x - 5)=180$$

Step2: Simplify the left - hand side

Combine like terms.
$$2x+4x+25 - 5=180$$
$$6x + 20=180$$

Step3: Isolate the variable term

Subtract 20 from both sides.
$$6x=180 - 20$$
$$6x=160$$

Step4: Solve for x

Divide both sides by 6.
$$x=\frac{160}{6}=\frac{80}{3}$$

Step5: Find $\angle7$

Substitute $x = \frac{80}{3}$ into the expression for $\angle7$.
$$\angle7=2x + 25=2\times\frac{80}{3}+25=\frac{160}{3}+25=\frac{160 + 75}{3}=\frac{235}{3}\approx78.33^{\circ}$$

Step6: Find $\angle8$

Substitute $x=\frac{80}{3}$ into the expression for $\angle8$.
$$\angle8=4x - 5=4\times\frac{80}{3}-5=\frac{320}{3}-5=\frac{320 - 15}{3}=\frac{305}{3}\approx101.67^{\circ}$$

Answer:

$x=\frac{80}{3}$, $\angle7=\frac{235}{3}^{\circ}\approx78.33^{\circ}$, $\angle8=\frac{305}{3}^{\circ}\approx101.67^{\circ}$