Question

homework mon feb 9, due tue feb 10

1. find the value of x.

x = ________

1. find the value of x and y.

x = ______ y = ______

1. name a pair of vertical angles.
2. name a pair of supplementary angles.

40°
3x-10°
16°
3y + 89
2x

Explanation:

Step1: Set up right angle equation

The two angles sum to $90^\circ$.
$40 + (3x - 10) = 90$

Step2: Simplify and solve for x

Combine constants, isolate x.
$3x + 30 = 90$
$3x = 60$
$x = 20$

Step3: Set vertical angles equal for x

Angle $a$ and angle $c$ are vertical angles.
$2x = 16$

Step4: Solve for x

Isolate x.
$x = 8$

Step5: Set vertical angles equal for y

Angle $d$ and angle $b$ are vertical angles; angle $d$ and $a$ are supplementary.
$3y + 89 + 16 = 180$

Step6: Simplify and solve for y

Combine constants, isolate y.
$3y + 105 = 180$
$3y = 75$
$y = 25$

Step7: Identify vertical angles pair

Vertical angles are opposite intersecting lines.

Step8: Identify supplementary angles pair

Supplementary angles sum to $180^\circ$.

Answer:

1. $x = 20$
2. $x = 8$, $y = 25$
3. $\angle a$ and $\angle c$ (or $\angle b$ and $\angle d$)
4. $\angle a$ and $\angle d$ (or $\angle a$ and $\angle b$, $\angle b$ and $\angle c$, $\angle c$ and $\angle d$)