Angles

Using the same diagram (ABEF a square, BCDE a rectangle, with A, B, C on one straight line and F, E, D on another), ∠ACF = 35° and ∠DCE = 18°. Find ∠FCE.

  A                    B         C
  +--------------------+---------+
   \                        \35 /|
     \                       \ / | 18
       \                      X  |
  +------\---------------------\-+
  F       (to F)          E      D

  at C the whole angle from CA down to CD is 90 degrees

answer

The 8-point compass shows the houses of 8 children around point O: Perry north, Ziming north-east, Bill east, Hadi south-east, Ali south, Sam south-west, Dave west, Shawn north-west. Roy is at point O facing Perry’s house. How many degrees must he turn in a clockwise direction so that he can face Shawn’s house?

            Perry
   Shawn      |      Ziming
        \     |     /
  Dave -------O------- Bill
        /     |     \
    Sam       |       Hadi
             Ali

answer

Using a protractor, measure ∠ABC. BA runs horizontally to the left from B; BC rises steeply up and slightly to the right.

                              C
                             /
                            /
                           /
                          /
  A ---------------------/ B
                       (angle here)

  measure from BA, round to BC

answer

Rectangle PQRS is folded to form the figure below. ∠y is three times ∠x. Find ∠x.

  P                                     Q
  +-------------------------------------+
  |                                 y / :
  |                                  /  : x
  |                                 /   :
  |                            \   /    :
  +-----------------------------\-/-----+
  S                                     R

  the dashed line is where the corner R USED to be;
  the fold crease runs from Q

answer

A rectangular piece of paper PQRS was folded as shown below, so that the edge RQ came down onto the line RU. Find ∠TRU.

  P   T                                 Q
  +---+---------------------------------+
  |    \ \
  |     \   \
  U +    \      \
  |        \        \
  |         \          \  52 deg
  + - - - - - \- - - - - - +
  S                        R

  the dashed line S—R is where the bottom edge still is;
  TR is the crease

answer

Ben was standing at Point X. He turned 225° anti-clockwise and then made another 1/4-turn in the clockwise direction. He ended up facing the Bus Bay. Which location was Ben facing at first?

                     Library                     N
                        |                        ^
     General Office     |     Bus Bay            |
                 \      |      /
   Computer Lab ------- X ------- Field
                 /      |      \
     Dental Clinic      |     Basketball Court
                        |
                      Hall

(1) Hall   (2) Field   (3) Library   (4) Computer Lab

answer (1) (2) (3) (4)

A protractor is placed with its centre at Y and its baseline along the bottom. Two lines are drawn from Y: one up to the left towards X, reading 18° above the baseline, and one up to the right towards Z, reading 38° above the baseline. Find the value of ∠XYZ.

            Z
   X         /
     \      /
      \    /
  -----\--/---------  (the protractor baseline)
        \/
        Y

  X is 18 deg above the baseline on the LEFT
  Z is 38 deg above the baseline on the RIGHT

(A) 18°   (B) 38°   (C) 124°   (D) 142°

answer (A) (B) (C) (D)

Kayden is standing at point K facing the park. He makes a 135° clockwise turn followed by a 315° anticlockwise turn. Where will he be facing now?

            Shopping Centre                 North
                   |                          ^
    Library        |        Park              |
            \      |      /
   Cinema ---------K--------- Market
            /      |      \
  Food Centre      |       Playground
                   |
                 School

(A) Food Centre   (B) Cinema   (C) Market   (D) School

answer (A) (B) (C) (D)

In the figure, ABCD is a rectangle and DEFG is a square, overlapping at D. ∠CDG = 64° and ∠EDH = 33°, where DH is a straight line from D. Find ∠ADH.

        C            D            E
         \    64    / \    33    /
          \       /     \      /
           \    /   G     \  /  H
            \ /             \
             A

  at D, the rays run in the order  C, G, A, H, E
  rectangle corner ADC = 90 deg · square corner GDE = 90 deg

answer

The clock shown below was 45 minutes behind the actual time. To set the clock to the correct time, how many 1/4-turn(s) must the minute hand be moved clockwise?

        12
   11        1
 10            2
       |
  9    +---->   3      minute hand on 12
                       hour hand on 3
  8            4
    7        5
        6

(1) 1   (2) 2   (3) 3   (4) 4

answer (1) (2) (3) (4)

Helen was at a restaurant in a zoo. At the restaurant, Helen was facing south-west at first. She then made a 3/4-turn clockwise. Which animal would she be facing then?

                    Lion                        N
                     |                          ^
    Elephant         |         Tiger            |
            \        |        /
             \       |       /
   Zebra ---- RESTAURANT ---- Leopard
             /       |       \
            /        |        \
    Giraffe          |         Monkey
                     |
                  Penguin

(1) Lion   (2) Tiger   (3) Monkey   (4) Elephant

answer (1) (2) (3) (4)