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Numeracy Intermediate June 2017 Unit 1 Q7

WJECIntermediateCurrent spec6 marksAngles (Including Parallel Lines)Constructions

7. Kari is making a jigsaw puzzle.
She has designed the pattern on a piece of paper.
Kari plans to make each piece of the jigsaw a different colour.

Part of her plan is shown below.

Rectangle crossed by two parallel lines (marked with arrows) and two other lines, enclosing a four-sided piece labelled Red; angle 86° marked at the top left, side 6 cm, angle 72° at the right, side 8 cm along the lower parallel line

Diagram not drawn to scale

Kari now sketches a diagram of the red piece of the jigsaw, which is shown below.
She shows some extended lines and indicates all the angles she needs to find.

The red piece with extended lines: 86° outside the top-left corner with c the interior angle there, b the interior angle at the top-right corner, side 6 cm on the right, a the interior angle at the bottom-right corner with 72° vertically opposite it, side 8 cm along the bottom (parallel to the top side, arrows), d the interior angle at the bottom-left corner

Diagram not drawn to scale

Find the 4 missing angles in the red piece of the jigsaw.
Draw the red piece of Kari’s jigsaw accurately.
One side has been drawn for you. [6]

\(a\) = …………… °,   \(b\) = …………… °,   \(c\) = …………… °,   \(d\) = …………… °

Space for drawing the red piece of jigsaw:

A line segment labelled 8 cm, drawn at a slight upward slope

On screen this diagram may not be shown at actual size. To measure it, use the question paper (PDF) printed at 100%.