Reach for the Star

Circle geometry pathway · Optional extension

L081 · Allow 10–15 minutes for learners ready to move on. Answers are available after an attempt.

Stretch

A central angle is 146°. Find the circumference angle subtending the same arc.

Reveal a worked check after attempting

73°.

Deep challenge

In a cyclic quadrilateral, opposite angles are 2x+10 and 3x−5. Find x and both angles.

Reveal a worked check after attempting

5x+5=180, x=35; angles 80° and 100°.

Recall & Review: feedback and extension integration

Lesson L081: Circle geometry pathway

Objective: Use circle geometry at the appropriate tier and explain angle reasoning.

60-minute structure: 0-7 Connect & Check; 7-14 Share; 14-25 Present/model; 25-44 Apply route choice/practice; 44-52 independent exam-style check; 52-60 Recall & Review, WWW/EBI and next step.

What Went Well (WWW)

I selected the correct geometric fact, theorem, formula or transformation and used a clear diagram with appropriate labels and units.

Even Better If (EBI)

I will name the fact or theorem, show the substitution or construction step and check whether the size, direction and units of the result are reasonable.

Stretch and deep challenge

Stretch: A central angle is 146°. Find the circumference angle subtending the same arc.

Deep challenge: In a cyclic quadrilateral, opposite angles are 2x+10 and 3x−5. Find x and both angles.