An angle is formed by the intersection of two rays at a point. The point where the rays meet is the vertex of that angle and the two rays are called the arms of the angle.<\/span><\/p>\n Adjacent Angles<\/strong> are the angles that share a common vertex and a common arm.\u00a0<\/span><\/p>\n Adjacent Angles<\/i><\/b><\/p>\n <\/i><\/b><\/p>\n The above diagram depicts angles that are adjacent.<\/span><\/p>\n \u2220<\/span>COB and <\/span>\u2220<\/span>BOA are adjacent to each other, their common vertex is O and their common arm is OB.<\/span><\/p>\n <\/p>\n Some Properties of two adjacent angles are:<\/span><\/span><\/p>\n <\/p>\n Two angles are complementary if the sum of their angle measurement is 90<\/span>\u00b0<\/span>.<\/span><\/p>\n Complementary Adjacent Angles<\/i><\/b><\/p>\n In the figure above <\/span>\u2220<\/span>AOB and <\/span>\u2220<\/span>BOC are adjacent and complementary angles.<\/span><\/p>\n <\/p>\n <\/b><\/p>\n Two angles are supplementary if the sum of their angle measurement is 180<\/span>\u00b0<\/span>.<\/span><\/p>\n Supplementary Adjacent Angles<\/i><\/b><\/p>\n In the figure above <\/span>\u2220<\/span>CAD and <\/span>\u2220<\/span>DAE are adjacent and supplementary(linear) angles.<\/span><\/p>\n <\/span><\/p>\n Example<\/b>:<\/b> From the figure determine the angles that are adjacent. What is the angle measurement of <\/span>\u2220<\/span>BOC if <\/span>\u2220<\/span>AOD = 140<\/span>\u00b0<\/span>?<\/span><\/p>\n Solution<\/b>:<\/b>\u00a0<\/span><\/p>\n The two pairs of angles that are adjacent are:<\/span><\/p>\n \u2220<\/span>AOB and <\/span>\u2220<\/span>BOC; <\/span>\u2220<\/span>BOC and <\/span>\u2220<\/span>COD.<\/span><\/p>\n Given <\/span>\u2220<\/span>AOD = 140<\/span>\u00b0<\/span>, <\/span>\u2220<\/span>AOC = 45<\/span>\u00b0<\/span> , <\/span>\u2220<\/span>COD = 45<\/span>\u00b0<\/span>.<\/span><\/p>\n \u2220<\/span>AOD = <\/span>\u2220<\/span>AOC + <\/span>\u2220<\/span>BOC + <\/span>\u2220<\/span>COD<\/span><\/p>\n \u21d2 <\/span>140<\/span>\u00b0<\/span> = 45<\/span>\u00b0<\/span> + <\/span>\u2220<\/span>BOC\u00a0 + 45<\/span>\u00b0<\/span><\/p>\n \u2234 \u2220<\/span>BOC = 140<\/span>\u00b0<\/span> –<\/span> ( 45<\/span>\u00b0<\/span> + 45<\/span>\u00b0 <\/span>)<\/span><\/p>\n \u21d2 <\/span>\u2220<\/span>BOC = 140<\/span>\u00b0<\/span> –<\/span> 90<\/span>\u00b0<\/span> = 50<\/span>\u00b0.<\/span><\/p>\n Hence, the measurement of <\/span>\u2220<\/span>BOC = 50<\/span>\u00b0<\/span>.<\/span><\/p>\n <\/span><\/p>\n [\/et_pb_text][\/et_pb_column][et_pb_column type=”2_5″ module_id=”stickysideR” admin_label=”Column R” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fdefe0″ custom_padding=”25px|25px|25px|25px|true|true” sticky_position=”top” sticky_offset_top=”-280px” sticky_limit_top=”row” sticky_limit_bottom=”row” sticky_position_tablet=”none” sticky_position_phone=”none” sticky_position_last_edited=”on|desktop” sticky_limit_bottom_tablet=”” sticky_limit_bottom_phone=”” sticky_limit_bottom_last_edited=”on|phone” border_radii=”on|15px|15px|15px|15px” box_shadow_style=”preset3″ global_colors_info=”{}”][et_pb_image src=”https:\/\/eistudymaterial.s3.amazonaws.com\/1080×1080.png” alt=”Free Trial banner” title_text=”Mindspark Free Trial Banner” url=”https:\/\/mindspark.in\/free-trial” align=”center” module_class=”adsimg” _builder_version=”4.11.1″ _module_preset=”default” custom_padding=”||||false|false” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}” transform_styles__hover_enabled=”on|hover” transform_scale__hover_enabled=”on|hover” transform_translate__hover_enabled=”on|desktop” transform_rotate__hover_enabled=”on|desktop” transform_skew__hover_enabled=”on|desktop” transform_origin__hover_enabled=”on|desktop” transform_scale__hover=”102%|102%”][\/et_pb_image][et_pb_text admin_label=”Explore Other Topics [\/et_pb_text][et_pb_text _builder_version=”4.10.7″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\n [\/et_pb_text][et_pb_text admin_label=”Related Concepts [\/et_pb_text][et_pb_text _builder_version=”4.13.1″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\n![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/angle1-300x179.png\")
<\/span><\/p>\nProperties<\/b><\/h2>\n
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Complementary Adjacent Angles<\/b><\/h2>\n
![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/angle2-300x266.png\")
<\/span><\/p>\nSupplementary or Linear Adjacent Angles\u00a0<\/b><\/h2>\n
![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/angle3-300x145.png\")
<\/span><\/p>\n![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/angle4-257x300.png\")
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\n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\nExplore Other Topics<\/h1>\n
\n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\nRelated Concepts<\/h1>\n