PSLE PQRS and RUWT are identical parallelograms. VRQ and TSR are identical right-angled triangles.
- Find ∠x.
- Find ∠y.
- Select the words that describe QVU in the statement:
QVU (is/is not) a straight line because the sum of angles QVR and RVU (is/is not) 180° Give your answers in this format. (Eg is, is not)
(a)
∠x
= 180° - 74°
= 106° (Interior angles)
(b)
∠TRU
= ∠QRS
= 106° (Parallelogram)
∠QRV
= 180° - 90° - 26°
= 64° (Angles sum of triangle)
∠y
= 360° - 106° - 106° - 26° - 64°
= 58° (Angles at a point)
(c)
∠RVU
= 180° - 32° - 58°
= 90°
Since ∠RVU is 90°, it adds up to 180° with ∠QVR to form a straight line. So, QVU
is a straight line because the sum of angles QVR and RVU
is 180°.
Answer(s): (a) 106°; (b) 64°; (c) is, is