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Geometry
Geometry

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Question 1

Find the unknown angles in each of these diagrams, which represent part of the bracing structure supporting a marquee.

Answer

  • (a) In ΔABC,

    therefore

  • (b) In ΔFGH,

    therefore

    As EFG is a straight line,

    So

    In ΔEFH,

Question 2

Deduce the value of α in the triangle below.

Answer

Lines XY and XZ are of equal length. This means that the triangle is isosceles, so the base angles and are equal. Then

The third angle in the triangle is a right angle: .

Because the three angles in a triangle must add up to 180°,

Hence

Question 3

Find the unknown angles in the following isosceles triangles, which represent roof rafters.

Answer

  • (a) As this is an isosceles triangle, α = β.

    So

    Therefore

  • (b) As this is an isosceles triangle, γ = δ.

    So

    Therefore