LEARN · EXPLAIN · REVISE

A cyclic quadrilateral has one interior angle a°. Find its opposite interior angle.

Read the idea, work independently, then explain what changed.

2027 JM01 考試大綱 · 12. Rectilinear figures and circles · PDF 3 / printed page 3

TOPIC 01

Euclidean figures and circle theorems

Use similarity, angle and circle theorems with labeled points and compatible arcs.

Use similarity, angle and circle theorems with labeled points and compatible arcs.
Justify the method and check the conditions in a new situation.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Standard#Worked example

a=23

Inscribed-angle comparisons must subtend the same arc on the stated side; cyclic opposite angles sum to 180°.

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Identify the relevant geometric theorem and verify its hypotheses.

Hint 2

Opposite angles sum to 180^\circ.

Worked solution

The requested value is 157.

Checks and common pitfalls: It is the opposite angle, not an adjacent angle.

Think first. Reveal a hint when the class is ready.

Teacher preparation and assessment

Use similarity, angle and circle theorems with labeled points and compatible arcs.
Which condition is essential in euclidean figures and circle theorems?
Do similar triangles with doubled sides have doubled areas?

Model or definition: Use similarity, angle and circle theorems with labeled points and compatible arcs.
$\text{similarity length ratio }k\Rightarrow\text{area ratio }k^2$
Conditions: Inscribed-angle comparisons must subtend the same arc on the stated side; cyclic opposite angles sum to 180°.