A cyclic quadrilateral has two opposite angles (3x + 20)^° and (x + 40)^°. What is the larger of these two angles?

Worked solution for TMUA-P1-MM3-011 is revealed on this page behind the solution details.

Why isn't the answer to TMUA-P1-MM3-011 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM3-011 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM3-011?

No — calculators are banned in the TMUA. TMUA-P1-MM3-011 is set for a no-calculator target of about 240 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1-MM3-011?

TMUA-P1-MM3-011 is Paper P1 · Coordinate geometry in the (x,y)-plane (specification code MM3), level 3. Drill more of the same topic from this page.

TMUA-P1-MM3-011 — Paper P1 · Coordinate geometry in the (x,y)-plane · Level 3

P1MM3Level 3~240s target

Spec: MM3 · No calculator · ~240s

A cyclic quadrilateral has two opposite angles

(3x + 20)^\circ

and

(x + 40)^\circ

. What is the larger of these two angles?

Options

$70$
$90$
$100$
$110$
$130$

Letters only — the answer key is hidden. Work it out, then check the solution below.

Hint (check trope)

No written hint yet — check the trope: cyclic-quadrilateral, wrong-angle-trap. Name the trap first, work the stem by hand, then open the solution below.

Show solution

Opposite angles of a cyclic quadrilateral sum to

180^\circ

(3x + 20) + (x + 40) = 180

gives

x = 30

. The larger angle is

3(30) + 20 = 110

. Trap:

70^\circ

is the smaller angle — plausible if you solve for

x

correctly but answer the wrong angle.

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Keep practising

Same topic · same level

P1MM3Level 3

TMUA-P1-MM3-010

The line y = x + 1 crosses the circle x^2 + y^2 = 25 at two points. What is the length of the chord joining them?

Coordinate geometry in the (x,y)-plane

Open TMUA-P1-MM3-010 →

Same trap: cyclic-quadrilateral

P1MM3Level 2

TMUA-P1X-MM3-04

A cyclic quadrilateral has two opposite angles (2x + 10)^° and (3x + 15)^°. What is the larger of these two angles?

Coordinate geometry in the (x,y)-plane

Open TMUA-P1X-MM3-04 →

TMUA-P1-MM3-011 — Paper P1 · Coordinate geometry in the (x,y)-plane · Level 3

Options

Keep practising

Master Coordinate geometry in the (x,y)-plane

TMUA-P1-MM3-011 — Paper P1 · Coordinate geometry in the (x,y)-plane · Level 3

Options

Keep practising

Master Coordinate geometry in the (x,y)-plane