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In the adjoining figure, name the following pairs of angles.
$(i)$ Obtuse vertically opposite angles
$(ii)$ Adjacent complementary angles
$(iii)$ Equal supplementary angles
$(iv)$ Unequal supplementary angles
$(v)$ Adjacent angles that do not form a linear pair"
To do:
We have to name
(i) Obtuse vertically opposite angles
(ii) Adjacent complementary angles
(iii) Equal supplementary angles
(iv) Unequal supplementary angles
(v) Adjacent angles that do not form a linear pair
Solution:
(i) Angles greater than $90^o$ and form a pair of vertically opposite angles are called Obtuse vertically opposite angles.
Therefore,
$\angle BOC$ and $\angle AOD$ are obtuse vertically opposite angles.
(ii) Angles that have a common vertex, one common arm and non-common arms on either sides of the common arm and whose sum equal $90^o$ are called Adjacent complementary angles.
Therefore,
$\angle AOB$ and $\angle AOE$ are adjacent complementary angles.
(iii) Supplementary angles which are equal are called Equal supplementary angles.
Therefore,
$\angle EOB$ and $\angle EOD$ are equal supplementary angles.
(iv) Supplementary angles which are unequal are called Unequal supplementary angles.
Therefore,
$\angle EOA$ and $\angle EOC$ are unequal supplementary angles.
(v) $\angle AOB$ and $\angle AOE$, $\angle AOE$ and $\angle EOD$, $\angle EOD$ and $\angle COD$ are adjacent angles that do not form a linear pair.
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