{"id":5274,"date":"2021-12-04T08:19:32","date_gmt":"2021-12-04T08:19:32","guid":{"rendered":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/?page_id=5274"},"modified":"2022-01-03T07:53:32","modified_gmt":"2022-01-03T07:53:32","slug":"angle-sum-property-of-a-triangle","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/angle-sum-property-of-a-triangle\/","title":{"rendered":"ANGLE SUM PROPERTY OF A TRIANGLE"},"content":{"rendered":"

[et_pb_section fb_built=”1″ admin_label=”Section” module_class=”mainsec” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#e0f2fd” z_index=”1″ custom_padding=”5px||5px||true|false” locked=”off” collapsed=”off” global_colors_info=”{}”][et_pb_row column_structure=”3_5,2_5″ custom_padding_last_edited=”on|phone” _builder_version=”4.10.8″ _module_preset=”default” background_color=”#FFFFFF” width=”100%” max_width=”1310px” custom_padding=”|51px|40px|51px|false|true” custom_padding_tablet=”” custom_padding_phone=”|40px|30px|40px|false|true” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}”][et_pb_column type=”3_5″ admin_label=”Column L” _builder_version=”4.9.10″ _module_preset=”default” global_colors_info=”{}”][et_pb_text admin_label=”Acute Angles
\n” _builder_version=”4.11.3″ _module_preset=”default” header_font=”|700|||||||” header_text_align=”left” header_font_size=”50px” header_line_height=”1.18em” custom_padding=”|0px||4px|false|false” header_font_size_tablet=”” header_font_size_phone=”35px” header_font_size_last_edited=”on|phone” global_colors_info=”{}”]<\/p>\n

ANGLE SUM PROPERTY OF A TRIANGLE<\/h1>\n

[\/et_pb_text][et_pb_text admin_label=”Text” _builder_version=”4.13.1″ _module_preset=”default” text_font_size=”16px” header_2_font=”|600|||||||” header_2_text_color=”#a01414″ header_3_font=”|600|||||||” custom_padding=”15px|15px|54px|4px|false|false” global_colors_info=”{}”]<\/p>\n

ANGLE SUM PROPERTY OF A TRIANGLE\u00a0<\/b><\/h2>\n

A triangle is a polygon that has three sides and three interior angles. It is the smallest polygon. It has three vertices. It can be an acute, obtuse or right-angled triangle. The sum of the interior angles will always remain 180 degrees. The angle sum property of a triangle is one of the most frequently used properties in geometry and is used to calculate unknown angles.<\/span><\/p>\n

It states that the sum of interior angles of a triangle is 180 degrees<\/b>.<\/span><\/p>\n

 <\/p>\n

PROPERTIES OF A TRIANGLE<\/b><\/h2>\n

There are various properties of a triangle.<\/span><\/p>\n

    \n
  1. A triangle has three sides, three vertices and three angles.<\/span><\/li>\n
  2. The sum of all the angles inside of a triangle is always equal to 180 degrees. It does not matter which kind of a triangle it is.<\/span><\/li>\n
  3. The sum of the length of any of the two sides of a triangle will always be greater than the length of the third side.<\/span><\/li>\n
  4. The side which is opposite to the largest angle of a triangle is the largest.<\/span><\/li>\n
  5. An exterior angle (angle outside the triangle) of the triangle is equal to the sum of the opposite interior angles. This is also known as the exterior angle property of a triangle.<\/span><\/li>\n<\/ol>\n

     <\/p>\n

    PROOF OF THE PROPERTY<\/b><\/h3>\n

    Let us consider the triangle ABC where AB, BC and AC are sides of a triangle. <\/span>\u2220<\/span>ABC, <\/span>\u2220<\/span>BCA and <\/span>\u2220<\/span>BAC are the interior angles of a triangle.\u00a0<\/span><\/p>\n

    \"\"<\/span><\/p>\n

    Proof:<\/b> Draw a line PQ parallel to the base of the triangle BC.\u00a0<\/span><\/p>\n

    PQ is a straight line so <\/span>\u2220<\/span>PAB +<\/span>\u2220<\/span>BAC + <\/span>\u2220<\/span>QAC = 180\u00b0\u00a0 <\/span> ——-(1)<\/span><\/p>\n

    We also know that, <\/span>\u2220<\/span>PAB = <\/span>\u2220<\/span>ABC and <\/span>\u2220<\/span>QAC = <\/span>\u2220<\/span>BCA (Since PQ is parallel to BC and AB is the transversal; Corresponding angles are equal when a transversal intersects parallel lines)<\/span><\/p>\n

    Substituting the values of <\/span>\u2220<\/span>PAB and <\/span>\u2220<\/span>QAC in equation (1)<\/span><\/p>\n

    \u2220<\/span>ABC +<\/span>\u2220<\/span>BAC + <\/span>\u2220<\/span>BCA\u00a0 = 180\u00b0<\/span><\/p>\n

    Hence proved.\u00a0<\/span><\/span><\/p>\n

    <\/span><\/p>\n

    Examples\u00a0<\/b><\/h2>\n

    <\/b><\/p>\n

    1. If in a triangle ABC, <\/b>\u2220<\/b>A = 38\u00b0, <\/b>\u2220<\/b>B = 96\u00b0. Then what is the value of <\/b>\u2220<\/b>C?<\/b><\/h3>\n

    Since the sum of all the angles inside a triangle\u00a0 is 180\u00b0 so:<\/span><\/p>\n

    \u2220<\/span>A + <\/span>\u2220<\/span>B + <\/span>\u2220<\/span>C = 180\u00b0<\/span><\/p>\n

    \u21d2 38\u00b0 + 96\u00b0 + <\/span>\u2220<\/span>C = 180\u00b0<\/span><\/p>\n

    \u21d2 \u2220<\/span>C = 180\u00b0 – 134\u00b0<\/span><\/p>\n

    \u00a0 \u2234 \u2220<\/span>C = 46\u00b0<\/span><\/p>\n

    <\/span><\/p>\n

    2. In a triangle PQR, What is the value of <\/b>\u2220<\/b>P in a triangle which is right-angled at Q and <\/b>\u2220<\/b>R = 35\u00b0?<\/b><\/p>\n

    We know that, <\/span>\u2220<\/span>P + <\/span>\u2220<\/span>Q + <\/span>\u2220<\/span>R = 180\u00b0.<\/span><\/p>\n

    \u2220<\/span>P + 90\u00b0 + 35\u00b0 = 180\u00b0<\/span><\/p>\n

    \u21d2 \u2220<\/span>P = 180\u00b0 – 125\u00b0<\/span><\/p>\n

    \u2234 \u2220<\/span>P = 55\u00b0<\/span><\/p>\n

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    Explore Other Topics<\/h1>\n

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    [\/et_pb_text][et_pb_text admin_label=”Related Concepts
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    Related Concepts<\/h1>\n

    [\/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

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    Frequently Asked Questions\u00a0<\/span><\/span><\/h1>\n
      <\/ol>\n

      Q1: What is the angle sum property of a triangle?
      <\/strong><\/h3>\n

      Ans: <\/strong>The property states that the sum of all the interior angles of a triangle is 180\u00b0.
      <\/strong><\/span><\/span><\/p>\n

      Q2. Which side of the triangle is always the largest side?
      <\/strong><\/h3>\n

      Ans: <\/strong>The side which is opposite to the largest angle is the largest side of the triangle.
      <\/strong>
      <\/strong><\/p>\n

      [\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"

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