{"id":28255,"date":"2025-06-20T11:21:14","date_gmt":"2025-06-20T11:21:14","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=28255"},"modified":"2025-06-20T11:21:16","modified_gmt":"2025-06-20T11:21:16","slug":"find-all-missing-angles","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/find-all-missing-angles\/","title":{"rendered":"Find all missing angles"},"content":{"rendered":"\n

Gina Wilson all things algebra, Pls help! Name: Unit 4: Congruent Triangles Homework 2: Angles of Triangles Date: Bell: Directions: Find all missing angles: 152 115 m\u00e2\u201a\u0081 m\u00e2\u201a\u0081 MZ\u00e2\u201a\u0081 = mz\u00e2\u201a\u0081 = m\u00e2\u201a\u0081 = m\u00e2\u201a\u201a = m\u00e2\u201a\u0192 = m\u00e2\u201a\u201a = 118 m\u00e2\u201a\u0192 mZ\u00e2\u201a\u0081 m\u00e2\u201a\u201a = m\u00e2\u201a\u0192 = m\u00e2\u201a\u201e = m\u00e2\u201a\u2026 = mZ\u00e2\u201a\u2020 = m\u00e2\u201a\u2021 MZI = m\u00e2\u201a\u0081\u00e2\u201a\u201a = m\u00e2\u201a\u201a\u00e2\u201a\u0192 m\u00e2\u201a\u0081Z\u00e2\u201a\u201e m\u00e2\u201a\u2026 = Directions: Find the value of 1 (31 – 5)\u00c2\u00b2 (10T – 41)\u00c2\u00b2 471 – 5)\u00c2\u00b2 (3T + 1)\u00c2\u00b2 10. 11. (11-1)\u00c2\u00b2 (4 -13)\u00c2\u00b2 (201 – 3)\u00c2\u00b2 (41 + 13)\u00c2\u00b2 (61 + 2)\u00c2\u00b2<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

PART A: Finding Missing Angles<\/strong><\/p>\n\n\n\n

We\u2019ll use the triangle angle sum theorem: the interior angles of a triangle always add up to 180\u00b0.<\/p>\n\n\n\n

Here are a few solved problems based on your worksheet image:<\/p>\n\n\n\n

    \n
  1. 76\u00b0+59\u00b0+\u22201=180\u00b076\u00b0 + 59\u00b0 + \\angle 1 = 180\u00b0 \u2003\u22201=180\u00b0\u2212(76\u00b0+59\u00b0)=45\u00b0\\angle 1 = 180\u00b0 – (76\u00b0 + 59\u00b0) = 45\u00b0<\/li>\n\n\n\n
  2. 62\u00b0+67\u00b0+\u22201=180\u00b062\u00b0 + 67\u00b0 + \\angle 1 = 180\u00b0 \u2003\u22201=180\u00b0\u2212129\u00b0=51\u00b0\\angle 1 = 180\u00b0 – 129\u00b0 = 51\u00b0<\/li>\n\n\n\n
  3. 152\u00b0+115\u00b0+\u22201=180\u00b0152\u00b0 + 115\u00b0 + \\angle 1 = 180\u00b0 \u2003This seems off, as the given sum exceeds 180\u00b0. Possibly an exterior angle situation or an error in setup.<\/li>\n<\/ol>\n\n\n\n

    Now for a problem with three unknowns (Example 4): Given: \u22201=50\u00b0\\angle 1 = 50\u00b0, \u22202=42\u00b0\\angle 2 = 42\u00b0 So, \u22203=180\u00b0\u2212(50\u00b0+42\u00b0)=88\u00b0\\angle 3 = 180\u00b0 – (50\u00b0 + 42\u00b0) = 88\u00b0<\/p>\n\n\n\n

    PART B: Solving for <\/strong>xx<\/p>\n\n\n\n

    Let\u2019s look at problem 10 from the image: (11x\u22121)+(20x\u22123)+151=180(11x – 1) + (20x – 3) + 151 = 180<\/p>\n\n\n\n

    Simplify:<\/p>\n\n\n\n

    31x+147=18031x=33x=333131x + 147 = 180 \\\\ 31x = 33 \\\\ x = \\frac{33}{31}<\/p>\n\n\n\n

    You found the value of xx that ensures all three angle expressions together sum to 180\u00b0.<\/p>\n\n\n\n

    Why it Works (Explanation)<\/strong><\/p>\n\n\n\n

    The triangle angle sum theorem stems from Euclidean geometry. When we draw a straight line parallel to one side of the triangle through the opposite vertex, alternate interior angles are formed. These match the triangle’s internal angles, and since a straight line measures 180\u00b0, the internal angles must also add up to 180\u00b0. This rule helps in algebraic contexts too, where angles are given as expressions in xx. Solving the resulting equation reveals the value of xx, allowing you to find each angle’s true measure.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    Gina Wilson all things algebra, Pls help! Name: Unit 4: Congruent Triangles Homework 2: Angles of Triangles Date: Bell: Directions: Find all missing angles: 152 115 m\u00e2\u201a\u0081 m\u00e2\u201a\u0081 MZ\u00e2\u201a\u0081 = mz\u00e2\u201a\u0081 = m\u00e2\u201a\u0081 = m\u00e2\u201a\u201a = m\u00e2\u201a\u0192 = m\u00e2\u201a\u201a = 118 m\u00e2\u201a\u0192 mZ\u00e2\u201a\u0081 m\u00e2\u201a\u201a = m\u00e2\u201a\u0192 = m\u00e2\u201a\u201e = m\u00e2\u201a\u2026 = mZ\u00e2\u201a\u2020 = m\u00e2\u201a\u2021 MZI […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-28255","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/28255","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=28255"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/28255\/revisions"}],"predecessor-version":[{"id":28258,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/28255\/revisions\/28258"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=28255"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=28255"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=28255"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}