Angles in triangles and quadrilaterals

In triangle ABC, angle A = 48° and angle B = 71°.

Work out the size of angle C.

Three of the angles in a quadrilateral are 85°, 110° and 72°.

Work out the size of the fourth angle.

Ella says, “I can draw a triangle with angles of 65°, 58° and 67°.”

Is Ella correct? You must show your working.

The diagram shows triangle ABC.

1. Use a protractor to measure angle ABC.
2. Use a protractor to measure angle ACB.
3. Write down the special name for this type of triangle. Give a reason for your answer.

In triangle ABC, angle A = 54° and angle B = 67°.

The side BC is extended to the point D, so that BCD is a straight line.

1. Work out the size of angle ACB.
2. Work out the size of angle ACD. Give a reason for your answer.

D is a point on the side BC of triangle ABC, so BDC is a straight line.

Angle ADB = 112° and angle ACB = 35°.

1. Work out the size of angle ADC. Give a reason for your answer.
2. Work out the size of angle DAC. Give a reason for your answer.

ABCD is a quadrilateral. The diagonal AC splits it into two triangles, ABC and ACD.

In triangle ABC, angle BAC = 40° and angle ABC = 75°.

In triangle ACD, angle CAD = 52° and angle ADC = 84°.

1. Work out the size of angle ACB.
2. Work out the size of angle ACD.
3. Work out the size of angle BCD.

PQRS is a quadrilateral.

Angle P = 102°, angle Q = 64° and angle R = 98°.

The side PS is extended to the point T, so that PST is a straight line.

1. Work out the size of angle PSR. Give a reason for your answer.
2. Work out the size of angle RST. Give a reason for your answer.

In triangle ABC,

angle A = 2x°, angle B = (3x + 10)° and angle C = (90 − x)°.

Work out the size of the largest angle in the triangle.

PQRS is a parallelogram.

Angle P = (3x + 15)° and angle Q = (2x − 10)°. Angles P and Q are next to each other on the same side of the parallelogram.

Work out the value of x. Give a reason for each stage of your working.

The four angles of a quadrilateral are 74°, 101°, 2t° and (t + 5)°.

Work out the size of the largest angle of the quadrilateral.

ABCD is a square.

Triangle CDE is an equilateral triangle drawn on the side CD, outside the square.

1. Work out the size of angle ADE.
2. DA = DE, so triangle ADE is isosceles. Work out the size of angle DAE.

ABC is a straight line. The point D lies above the line.

Triangle BCD is isosceles with BD = CD.

Angle DBA = 134°.

Work out the size of angle BDC. Give a reason for each stage of your working.

The angles of a triangle are in the ratio 2 : 3 : 7.

Show that the triangle contains an obtuse angle.

ABCD is a quadrilateral with AB = AD and CB = CD. So ABCD is a kite.

Angle BAD = 76° and angle BCD = 118°.

Work out the size of angle ABC. Give reasons for your answer.

PQR is a triangle. The side PQ is extended to the point S.

Angle RQS = 112° and angle QPR = 44°.

Show that triangle PQR is isosceles. Give a reason for each stage of your working.

Triangle ABC is isosceles with AB = AC.

angle A : angle B = 2 : 5

Work out the size of angle A.

Triangle ABC is isosceles with AB = AC. Angle BAC = 48°.

D is a point on AC such that BD = BC.

Work out the size of angle ABD. Give a reason for each step of your working.

One angle of an isosceles triangle is 40°.

Work out the possible sizes of the other two angles of the triangle.

You must show that you have considered every possible case.