Let’s solve each problem step by step.
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Problem 10:
A chord and a tangent form an angle of 63° at the point of tangency. What is the measure of the arc intercepted by the chord?
→ When a tangent and a chord meet at the point of tangency, the angle they form is
half the measure of the intercepted arc.
So:
Angle = (1/2) × Intercepted Arc
63° = (1/2) × Arc
Multiply both sides by 2:
Arc = 126°
✔ Final Answer for #10:
126°
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Problem 11:
The minor arc in circle A has measure 85°. What is the measure of the angle formed by the chord and the tangent line?
→ Again, use the same rule:
Angle between tangent and chord = (1/2) × intercepted arc
Intercepted arc = 85°
So angle = (1/2) × 85° = 42.5°
✔ Final Answer for #11:
42.5°
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Problem 12:
In circle C, m∠ABC = 70°. Find mAC.
Looking at the diagram (even though we don’t describe it), ABC is likely an inscribed angle intercepting arc AC.
→ Inscribed Angle Theorem:
Measure of inscribed angle = (1/2) × measure of intercepted arc
So:
70° = (1/2) × mAC
Multiply both sides by 2:
mAC = 140°
✔ Final Answer for #12:
140°
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Problem 13:
In circle D, m∠EDF = 90°. Find mEF.
Again, assuming ∠EDF is an inscribed angle intercepting arc EF.
Then:
90° = (1/2) × mEF
→ mEF = 180°
That makes sense — if the inscribed angle is 90°, it intercepts a semicircle.
✔ Final Answer for #13:
180°
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Final Answer:
10. 126°
11. 42.5°
12. 140°
13. 180°
Parent Tip: Review the logic above to help your child master the concept of geometry 10 4 worksheet answers.
