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

Worked solution for TMUA-P1X-MM3-04 is revealed on this page behind the solution details.

Why isn't the answer to TMUA-P1X-MM3-04 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1X-MM3-04 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1X-MM3-04?

No — calculators are banned in the TMUA. TMUA-P1X-MM3-04 is set for a no-calculator target of about 180 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1X-MM3-04?

TMUA-P1X-MM3-04 is Paper P1 · Coordinate geometry in the (x,y)-plane (specification code MM3), level 2. Drill more of the same topic from this page.

TMUA-P1X-MM3-04 — Paper P1 · Coordinate geometry in the (x,y)-plane · Level 2

P1MM3Level 2~180s target

Spec: MM3 · No calculator · ~180s

A cyclic quadrilateral has two opposite angles

(2x + 10)^\circ

and

(3x + 15)^\circ

. What is the larger of these two angles?

Options

$72^\circ$
$108^\circ$
$90^\circ$
$100^\circ$
$180^\circ$

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

(2x + 10) + (3x + 15) = 180

gives

x = 31

. The angles are

72

and

108

, so the larger is

108^\circ

. Trap:

72^\circ

is the smaller angle — plausible if you solve for

x

correctly but answer the wrong angle.

Keep practising

Same topic · same level
P1MM3Level 2
TMUA-P1-MM3-001
In an arithmetic sequence the 3rd term is 11 and the 8th term is 31. What is the first term?
Coordinate geometry in the (x,y)-plane
Open TMUA-P1-MM3-001 →
Same trap: cyclic-quadrilateral
P1MM3Level 3
TMUA-P1-MM3-011
A cyclic quadrilateral has two opposite angles (3x + 20)^° and (x + 40)^°. What is the larger of these two angles?
Coordinate geometry in the (x,y)-plane
Open TMUA-P1-MM3-011 →
Step up a 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 →

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Keep practising

Same topic · same level

P1MM3Level 2

TMUA-P1-MM3-001

In an arithmetic sequence the 3rd term is 11 and the 8th term is 31. What is the first term?

Coordinate geometry in the (x,y)-plane

Open TMUA-P1-MM3-001 →

Same trap: cyclic-quadrilateral

P1MM3Level 3

TMUA-P1-MM3-011

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

Coordinate geometry in the (x,y)-plane

Open TMUA-P1-MM3-011 →

Step up a 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 →

TMUA-P1X-MM3-04 — Paper P1 · Coordinate geometry in the (x,y)-plane · Level 2

Options

Keep practising

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

TMUA-P1X-MM3-04 — Paper P1 · Coordinate geometry in the (x,y)-plane · Level 2

Options

Keep practising

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