Problem preview
G-C.3 Warmup M2-031-A11-V01

Construct inscribed/circumscribed circles of triangles and prove angle properties of cyclic quadrilaterals.

Solve for a variable using supplementary opposite angles in a cyclic quadrilateral

Problem

Solve for the variable in cyclic quadrilateral \(ABCD\) with opposite angles \(3x+20^{\circ}\) and \(100^{\circ}\).

Big Picture

What this problem is really about

The algebra comes after the geometry: first confirm that the variable angle and the given angle are at opposite vertices of a cyclic quadrilateral. We’ll set their expressions to a supplementary sum, solve the linear equation, and then substitute back to verify.

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Four variants of this problem type
Curriculum context
Course
Math II
Standard
G-C.3
Category
Geometry
Domain
Circles
Objective
Construct inscribed/circumscribed circles of triangles and prove angle properties of cyclic quadrilaterals.
Problem type
Solve for a variable using supplementary opposite angles in a cyclic quadrilateral