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					Question

Calculate the value of the pronominal in the diagram below showing.




Solution




Extend the line BO from the point O so that it cuts the ray AC at E.




In the line BE,

Since the angles in a linear pair are supplementary

78° + X° = 180°

X° = 180° – 78°

X° = 102°

We know that,

Sum of angles in a triangle is 180°.

58° + X° + Y° = 180°
58° + 102° + Y° = 180°

160° + Y° = 180°

Y° = 180° – 160°

Y° = 20°




Just extend the line BF from B.

Now using the Alternate Interior Angle Theorem

We can prove that Alternate Interior Angles are equal.

3a + 2 = 20°

Since BE is a traversal cutting the two parallel lines

Hence (3a +2) and 20 are congruent

3a + 2 = 20°

3a = 18°

a = 18°/3

a = 6°.

				
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posted:5/30/2012
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