CIE Mathematics Paper-1: Specimen Questions 134 - 135 of 175

Question number: 134

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A square ABCD has two diagonals, O is center. Angle ODA = 450 . Calculate angle OAD.

A square is making four triangles in it

A square is making four triangles in it

Find the angle OAD by using given angle and logic

Explanation

Here,

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

Angle ADO = 450 , as we know angle made by intersecting of diagonal is 900, so angle AOD = 900.

Now, in any triangle addition of all angles will give 1800.

So, in AOD, OAD+ADO+AOD=1800

OAD+450+900=1800

OAD=18001350

OAD=450 .

Question number: 135

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In the diagram, ABCD and a line LM passing through point D. Angle BDM=450 . 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

Find the angle LDB by using given angle and lines

Explanation

Here, ABCD and a line LM passing through point D.

Now, Angle BDM=450 is given.

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

So, angle ADL=450.

  • Now, angles BDM and CDM are complimentary angles, as shown in figure.
  • Two angles whose adding gives 900 are called as complimentary angles.

So, BDM+CDM=900CDM=900450CDM=450.

Now, ABCD , so CDA=900 .

So, angleLDB=BDM+CDM+CDA+ADL=450+450+900+450=2250

Thus, angle LDB=2250,ADL=450,CDM=450.

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