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Chapter 5 Lines and Angles Ex 5.1 Solutions

Question - 11 : - In the following figure, is тИа1 adjacent to тИа2? Give reasons.

Answer - 11 : -

No, тИа1 andтИа2 are not adjacent angles.

Reasons:
(i) тИа1 + тИа2 тЙа 180┬░
(ii) They have no common vertex.

Question - 12 : - Find the values of the angles x, y and z in each of the following:

Answer - 12 : -

From Fig. 1. we have
тИаx = тИа55┬░ (Vertically opposite angles)
тИаx + тИаy = 180┬░ (Adjacent angles)
55┬░ + тИаy = 180┬░ (Linear pair angles)
тИ┤ тИаy = 180┬░ тАУ 55┬░ = 125┬░
тИаy = тИаz (Vertically opposite angles)
125┬░ = тИаz
Hence, тИаx = 55┬░, тИаy = 125┬░ and тИаz = 125┬░
(ii) 25┬░ + x + 40┬░ = 180┬░ (Sum of adjacent angles on straight line)
65┬░ + x = 180┬░
тИ┤ x = 180┬░ тАУ 65┬░ = 115┬░
40┬░ + y = 180┬░ (Linear pairs)
тИ┤ y = 180┬░ тАУ 40┬░ = 140┬░
y + z = 180┬░ (Linear pairs)
140┬░ + z = 180┬░
тИ┤ z = 180┬░ тАУ 140┬░ = 40┬░
Hence, x тАУ 115┬░, y = 140┬░ and z тАУ 40┬░

Question - 13 : -
Fill in the blanks:
(i) If two angles are complementary, then the sum of their measures is ______ .
(ii) If two angles are supplementary, then the sum of their measures is ______ .
(iii) Two angles forming a linear pair are ______ .
(iv) If two adjacent angles are supplementary, they form a ______ .
(v) If two lines intersect at a point, then the vertically opposite angles are always ______ .
(vi) If two lines intersect at a point, and if one pair of vertically opposite angles are acute angles, then the other pair of vertically opposite angles are ______ .

Answer - 13 : -

(i) 90┬░
(ii) 180┬░
(iii) Supplementary
(iv) Linear pair
(v) Equal
(vi) Obtuse angle

Question - 14 : -
In the given figure, name the following pairs of angles.
┬а
(i) Obtuse vertically opposite angles.
(ii) Adjacent complementary angles.
(iii) Equal supplementary angles.
(iv) Unequal supplementary angles.
(v) Adjacent angles but do not form a linear pair.

Answer - 14 : -

(i) тИаBOC andтИаAOD areobtuse vertically opposite angles.
(ii) тИаAOB andтИаAOE areadjacent complementary angles.
(iii) тИаEOB andтИаEOD areequal supplementary angles.
(iv) тИаEOA andтИаEOC areunequal supplementary angles.
(v) тИаAOB andтИаAOE, тИаAOE and тИаEOD, тИаEOD andтИаCOD areadjacent angles but do not form a linear pair.

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