## Thursday, October 7, 2010

### Angle PSLE 2010 P2 Q13

In the figure below, ABC is a triangle. X, Y and Z are points on the triangle such that AX=AY and YB=ZB.

If angle AYZ=104⁰ and angle XYB=107⁰, find angle ZCX.

180  -  104  =  76

180  -  76  -  76  =  38

180  -  107  =  73

180  -  73  -  73  =  34

180  -  28  -  34  =  118⁰

It is  118°.

Alternative solution provided by P6 pupil

107° + 104°  =  211°

211°  -  180°  =  31°

360°  -  31°  -  107°  -  104°  =  118°

1. As appeared in PSLE 2010 exam:

In the figure below, ABC is a triangle. X, Y and Z are points on the triangle such that AX=AY and YB=ZB.
If angle AYZ=104⁰ and angle XYB=107⁰, find angle ZCX.

Diagram given:
ABC is a triangle with A at the left hand corner and goes clockwise passing B, C and back to A. CB is the base.
X is a point along line AC and is joined to a point Y which is along the line AB.
Z is a point along CB and is joined to point Y.
Both AX and AY are marked as equal in length.
Both YB and BZ are marked as equal in length.

2. 180-107=73
180-104=76
180-73=107
180-76=104
180-76-73=31
Total angles in a 4sided figure equals to 360 degrees
360-104-107-31=118