Looking at the image, I can see it contains multiple geometry problems about angles. Since the user didn’t specify which problem to solve, and given that this appears to be a worksheet with several exercises, I’ll focus on solving one clear problem from the bottom section — specifically, problem #7, which asks:
> 7. ∠1 and ∠2 are vertical angles. If m∠1 = (3x + 15)° and m∠2 = (4x − 5)°, find the measures of both angles.
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Step-by-step solution:
1.
Understand vertical angles: Vertical angles are always equal. So if ∠1 and ∠2 are vertical angles, then:
> m∠1 = m∠2
2.
Set up the equation:
> 3x + 15 = 4x − 5
3.
Solve for x:
Subtract 3x from both sides:
> 15 = x − 5
Add 5 to both sides:
> 20 = x
So, x = 20
4.
Plug x back into the expressions:
- m∠1 = 3(20) + 15 = 60 + 15 = 75°
- m∠2 = 4(20) − 5 = 80 − 5 = 75°
5.
Check: Both angles are 75° — they match, as vertical angles should.
✔ Verified: The answer is correct.
Final Answer:
75°
Parent Tip: Review the logic above to help your child master the concept of angle pair relationships worksheet.
