given m∠1 = 75°
∠1 and ∠2 are ______ m∠2 = ______
∠1 and ∠3 are ______ m∠3 = ______
∠1 and ∠5 are ______ m∠5 = ______
∠5 and ∠6 are ______ m∠6 = ______
∠5 and ∠7 are ______ m∠7 = ______
given m∠ybs = 130°
∠yus and ∠rbx are ______ m∠rbx = ______
∠ybs and ∠ydr are ______ m∠ydr = ______
∠ybs and ∠baq are ______ m∠baq = ______
∠baq and ∠pax are ______ m∠pax = ______
∠baq and ∠pab are ______ m∠pab = ______
given m∠g = 40°
∠g and ∠e are ______ m∠e = ______
∠g and ∠o are ______ m∠o = ______
∠g and ∠d are ______ m∠d = ______
∠g and ∠h are ______ m∠h = ______
∠e and ∠f are ______ m∠f = ______
∠e and ∠b are ______ m∠f = ______
∠e and ∠a are ______ m∠a = ______
fill in all of the missing angles for each set of parallel lines intersected by a transversal:
1.)
2.)
3.)
4.)
5.)
6.)

Question

Accepted Answer

### Top Section 1 (Given $m\angle1=75^\circ$)
# Explanation:
## Step1: Identify angle pair type
$\angle1$ and $\angle2$ are supplementary (linear pair).
$m\angle2 = 180^\circ - 75^\circ = 105^\circ$
## Step2: Identify angle pair type
$\angle1$ and $\angle3$ are vertical angles.
$m\angle3 = 75^\circ$
## Step3: Identify angle pair type
$\angle1$ and $\angle5$ are corresponding angles.
$m\angle5 = 75^\circ$
## Step4: Identify angle pair type
$\angle5$ and $\angle6$ are supplementary (linear pair).
$m\angle6 = 180^\circ - 75^\circ = 105^\circ$
## Step5: Identify angle pair type
$\angle5$ and $\angle7$ are vertical angles.
$m\angle7 = 75^\circ$
# Answer:
$\angle1$ and $\angle2$ are supplementary, $m\angle2=105^\circ$
$\angle1$ and $\angle3$ are vertical angles, $m\angle3=75^\circ$
$\angle1$ and $\angle5$ are corresponding angles, $m\angle5=75^\circ$
$\angle5$ and $\angle6$ are supplementary, $m\angle6=105^\circ$
$\angle5$ and $\angle7$ are vertical angles, $m\angle7=75^\circ$

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### Top Section 2 (Given $m\angle YBS=130^\circ$)
# Explanation:
## Step1: Identify angle pair type
$\angle YBS$ and $\angle RBX$ are vertical angles.
$m\angle RBX = 130^\circ$
## Step2: Identify angle pair type
$\angle YBS$ and $\angle YBR$ are supplementary (linear pair).
$m\angle YBR = 180^\circ - 130^\circ = 50^\circ$
## Step3: Identify angle pair type
$\angle YBS$ and $\angle BAQ$ are corresponding angles.
$m\angle BAQ = 130^\circ$
## Step4: Identify angle pair type
$\angle BAQ$ and $\angle PAX$ are vertical angles.
$m\angle PAX = 130^\circ$
## Step5: Identify angle pair type
$\angle BAQ$ and $\angle PAB$ are supplementary (linear pair).
$m\angle PAB = 180^\circ - 130^\circ = 50^\circ$
# Answer:
$\angle YBS$ and $\angle RBX$ are vertical angles, $m\angle RBX=130^\circ$
$\angle YBS$ and $\angle YBR$ are supplementary, $m\angle YBR=50^\circ$
$\angle YBS$ and $\angle BAQ$ are corresponding angles, $m\angle BAQ=130^\circ$
$\angle BAQ$ and $\angle PAX$ are vertical angles, $m\angle PAX=130^\circ$
$\angle BAQ$ and $\angle PAB$ are supplementary, $m\angle PAB=50^\circ$

---

### Top Section 3 (Given $m\angle g=40^\circ$)
# Explanation:
## Step1: Identify angle pair type
$\angle g$ and $\angle e$ are corresponding angles.
$m\angle e = 40^\circ$
## Step2: Identify angle pair type
$\angle g$ and $\angle a$ are corresponding angles.
$m\angle a = 40^\circ$
## Step3: Identify angle pair type
$\angle g$ and $\angle d$ are supplementary (same-side interior).
$m\angle d = 180^\circ - 40^\circ = 140^\circ$
## Step4: Identify angle pair type
$\angle g$ and $\angle h$ are supplementary (linear pair).
$m\angle h = 180^\circ - 40^\circ = 140^\circ$
## Step5: Identify angle pair type
$\angle e$ and $\angle f$ are supplementary (linear pair).
$m\angle f = 180^\circ - 40^\circ = 140^\circ$
## Step6: Identify angle pair type
$\angle e$ and $\angle b$ are supplementary (same-side interior).
$m\angle b = 180^\circ - 40^\circ = 140^\circ$
## Step7: Identify angle pair type
$\angle e$ and $\angle a$ are vertical angles.
$m\angle a = 40^\circ$
# Answer:
$\angle g$ and $\angle e$ are corresponding angles, $m\angle e=40^\circ$
$\angle g$ and $\angle a$ are corresponding angles, $m\angle a=40^\circ$
$\angle g$ and $\angle d$ are supplementary, $m\angle d=140^\circ$
$\angle g$ and $\angle h$ are supplementary, $m\angle h=140^\circ$
$\angle e$ and $\angle f$ are supplementary, $m\angle f=140^\circ$
$\angle e$ and $\angle b$ are supplementary, $m\angle b=140^\circ$
$\angle e$ and $\angle a$ are vertical angles, $m\angle a=40^\circ$

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### Bottom Section (Fill in Missing Angles)
# Explanation:
## 1.) Check parallel line validity
Lines $l$ and $m$ are not parallel (supplementary consecutive interior angles would sum to $180^\circ$; $113^\circ+67^\circ=180^\circ$, so they are parallel. Missing angles:
- Corresponding to $113^\circ$: $113^\circ$; supplementary to $113^\circ$: $67^\circ$
- Corresponding to $67^\circ$: $67^\circ$; supplementary to $67^\circ$: $113^\circ$
## 2.) Find $x$ and $y$
$x$ is supplementary to $130^\circ$ (same-side interior): $x=180^\circ-130^\circ=50^\circ$
$y$ is vertical to $130^\circ$: $y=130^\circ$
## 3.) Fill all angles
Given $47^\circ$, corresponding angles = $47^\circ$, vertical angles = $47^\circ$, supplementary angles = $180^\circ-47^\circ=133^\circ$
## 4.) Fill all angles
Given $24^\circ$, corresponding angles = $24^\circ$, vertical angles = $24^\circ$, supplementary angles = $180^\circ-24^\circ=156^\circ$
## 5.) Fill all angles
Given $111^\circ$, corresponding angles = $111^\circ$, vertical angles = $111^\circ$, supplementary angles = $180^\circ-111^\circ=69^\circ$
## 6.) Fill all angles
Given $65^\circ$ and $115^\circ$, corresponding angles match: $65^\circ$ on $q/r$, $115^\circ$ on $q/r$; supplementary pairs sum to $180^\circ$
# Answer:
1.) All missing angles: $113^\circ, 67^\circ, 113^\circ, 67^\circ$
2.) $x=50^\circ$, $y=130^\circ$
3.) All missing angles: $47^\circ, 133^\circ, 133^\circ, 47^\circ$
4.) All missing angles: $24^\circ, 156^\circ, 156^\circ, 24^\circ$
5.) All missing angles: $111^\circ, 69^\circ, 69^\circ, 111^\circ$
6.) All missing angles: $65^\circ, 115^\circ, 65^\circ, 115^\circ$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Top Section 1 (Given $m\angle1=75^\circ$)

Step1: Identify angle pair type

Step2: Identify angle pair type

Step3: Identify angle pair type

Step4: Identify angle pair type

Step5: Identify angle pair type

Step1: Identify angle pair type

Step2: Identify angle pair type

Step3: Identify angle pair type

Step4: Identify angle pair type

Step5: Identify angle pair type

Step1: Identify angle pair type

Step2: Identify angle pair type

Step3: Identify angle pair type

Step4: Identify angle pair type

Step5: Identify angle pair type

Step6: Identify angle pair type

Step7: Identify angle pair type

Answer:

Top Section 2 (Given $m\angle YBS=130^\circ$)