ANGLES

281 P4.AN.JM.17092871

Level 3
The figure shows a piece of square paper ABCD folded at two of its corners B and D. Given that ∠CFD = 81° and ∠BEC = 78°, find ∠BCD.

3 m

Attempt

282 P6.AN.NK.17051755

Level 3
In the figure, not drawn to scale, HIJ is equilateral triangle, HIJK and LMNP are identical rhombuses. Given that HI is parallel to PN, ∠MRS = 12° find ∠KRS.

3 m

Attempt

Equilateral triangle Rhombus Angles sum of triangle Corresponding angles

283 P4.AN.JM.17092847

Level 3
The figure shows a piece of rectangular paper ABCD folded at two of its corners C and D. ∠DFE is 6° larger than ∠CFG but it is half the size of ∠CFD. Find ∠CFD.

3 m

Attempt

Rectangle Angles on a straight line Overlapping angles Folded figure Model Comparison Units method

284 P6.AN.NK.17051750

Level 3
The figure is not drawn to scale. It shows a parallelogram TUVW and an isosceles triangle QTW next to it. ∠SWQ = 11°. SR and QP are straight lines. Find

∠z
∠x + ∠y
∠y

3 m

Attempt

Isosceles triangle Parallelogram Angles on a straight line Angles sum of triangle Corresponding angles

285 P5.AN.JM.17083126

Level 3
The figure shows two isosceles triangle ABC and ABD. Given that ∠ADB = 50° and ∠ACB = 84°, what is the value of ∠DAC?

3 m

Attempt

Isosceles triangle

286 P4.AN.JM.17092845

Level 3
The figure shows a piece of rectangular paper ABCD folded at one of its corners A. ∠AEB is 4 times as large as ∠AEF. Find ∠AEB.

3 m

Attempt

Rectangle Angles on a straight line Overlapping angles Folded figure Model Times-as-many Units method

287 P6.AN.NK.17051736

Level 3
In the figure, not drawn to scale, BA is parallel to DC and EF is parallel to AC. Find:

∠x
∠y

3 m

Attempt

Alternate angles Interior angles

288 P6.AN.NK.17051718

Level 3
In the figure, ABCD is a parallelogram. AC = CE = CF. AF and CE are straight lines. ∠AEC = 73° and ∠AFC = 34°. Find ∠ABC.

3 m

Attempt

Isosceles triangle Parallelogram Interior angles

289 P6.AN.NK.17051739

Level 3
The figure is not drawn to scale. KL//NM and ML//PK. Triangles KPL and LMN are isosceles triangles. Find

∠a
∠b.

3 m

Attempt

Isosceles triangle Angles sum of triangle Interior angles

290 P6.AN.NK.17051712

Level 3
In the figure, not drawn to scale, ABCD is a trapezium and PQCR is a square. AB//CQ. The size of ∠DCR is ⁵₄ of ∠DCQ . Find ∠ADC.

3 m

Attempt

Square Trapezium Interior angles Fraction of a whole Units method

291 P6.AN.NK.17051737

Level 3
The figure is not drawn to scale. It has three parallel lines and two isosceles triangles. ∠x and ∠y are in the ratio of 3 : 5 respectively. Find ∠x + ∠y + ∠z.

3 m

Attempt

Isosceles triangle Angles on a straight line Interior angles Ratio to units Units method

292 P6.AN.NK.17051719

Level 3
In the figure, ABCD is a trapezium. AZB is an isosceles triangle with AZ = BZ. AY and BX are straight lines. Find ∠DAZ.

3 m

Attempt

Isosceles triangle Trapezium Angles on a straight line Interior angles

293 P5.AN.JM.17083193

Level 2
In the figure, QOT and SOR are straight lines. ∠QOR = 152° and ∠TOP = 147°. Find ∠POR.

3 m

Attempt

Angles on a straight line

294 P6.AN.NK.17051724

Level 3
The figure is not drawn to scale. VWXY is a parallelogram. WZ and XZ are straight lines. UX = UW, ∠UWX = 57° and ∠UWV = 41°. Find the difference between ∠a and ∠b.