IGCSE Mathematics Paper-1: Specimen Questions with Answers 134 - 136 of 175

Question number: 134

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A square ABCD has two diagonals, O is center. Angle ODA = . Calculate angle OAD.

A square is making four triangles in it

A Square is Making Four Triangles in It

Explanation

Here,

As we can see in the figure AC and BD are intersecting lines in square.

Angle ADO = , as we know angle made by intersecting of diagonal is so angle AOD =

Now, in any triangle addition of all angles will give

So, in

.

Question number: 135

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In the diagram, and a line LM passing through point D. Angle . Find the angle LDB, CDM and ADL.

AB⊥CD and a line LM making an angle

AB⊥CD and a Line LM Making an Angle

Explanation

Here, and a line LM passing through point D.

Now, Angle is given.

  • So, angles BDM and ADL are vertical angles as shown in figure, which will be always same.

So, angle

  • Now, angles BDM and CDM are complimentary angles, as shown in figure.
  • Two angles whose adding gives are called as complimentary angles.

So,

Now, , so .

So,

Thus, angle

Question number: 136

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The diagram shows a regular pentagon and a square. Calculate the values of .

A regular pentagon and a square

A Regular Pentagon and a Square

Explanation

Here, pentagon is regular.

So, we can find it’s exterior angle by using the formula , where n = number of sides.

In pentagon number of sides = 5, so exterior angle =

So, as shown in figure, its interior angle .

Now, for angle :

As shown in figure, total angle is , so

.

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