Question

Work out the sizes of the ANGLES

Answer 1

r = 55°, s = 25°, t = 30°

Explanation:

The sum of the interior angles of a quadrilateral = 360°

Sum the 4 angles in the top quadrilateral and equate to 360

r + 100° + 110° + 95° = 360°

r + 305° = 360° ( subtract 305° from both sides )

r = 55°

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the 2 angles from 180° in the left triangle for s

s = 180° - (100 + 55)° = 180° - 155° = 25°

Similarly for the triangle on the right for t

t = 180° - 95 + 55)° = 180° - 150° = 30°

Answer 2

Explanation:

In quadrilateral ADEF

r + 95 +100 +110 = 360 {Sum of all angle of quadrilateral}

r + 305 = 360

r = 360 -305

r = 55

In triangle AEC,

r + 95 + t = 180

55 + 95 + t = 180

150 + t = 180

t = 180 -150

t = 30

In triangle ABD,

r +s + 100 = 180

55 + s + 100 = 180

s + 155 = 180

s = 180 - 155

s = 25