What is m\u2220DEF?
Enter your answer in the box.<\/p>\n\n\n\n
There is a triangle DEF in which side DE is congruent to side EF and G is the midpoint of the side DF. Segment EG intersect the side DF at point G. The measure of angle DEG is (3y+4) degrees and the measure of angle FEG is (5y-10) degrees.<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n The correct answer is: 130\u00a0degrees<\/strong><\/mark><\/p>\n\n\n\n To find the measure of angle ( m\u2220DEF ), we start by analyzing the given information about triangle ( DEF ). We know that sides ( DE ) and ( EF ) are congruent, which indicates that triangle ( DEF ) is isosceles. In an isosceles triangle, the angles opposite the congruent sides are equal. Therefore, we can say:<\/p>\n\n\n\n [ From the problem, we are given:<\/p>\n\n\n\n [ [ Since these angles are equal, we can set up the following equation:<\/p>\n\n\n\n [ Next, we solve for ( y ):<\/p>\n\n\n\n [ [ [ Now that we have the value of ( y ), we can substitute it back into the expressions for ( m\u2220DEG ) and ( m\u2220FEG ):<\/p>\n\n\n\n [ [ Since both angles ( DEG ) and ( FEG ) measure ( 25 ) degrees, we can find ( m\u2220DEF ) using the fact that the sum of angles in triangle ( DEF ) must equal ( 180 ) degrees.<\/p>\n\n\n\n Let ( m\u2220DEF = x ). Thus:<\/p>\n\n\n\n [ Substituting in the known values:<\/p>\n\n\n\n [ This simplifies to:<\/p>\n\n\n\n [ Subtracting ( 50 ) from both sides gives:<\/p>\n\n\n\n [ Therefore, the measure of angle ( m\u2220DEF ) is<\/p>\n\n\n\n [ This solution illustrates how we utilized properties of isosceles triangles and algebraic manipulation to determine the measures of the angles within triangle ( DEF ).<\/p>\n","protected":false},"excerpt":{"rendered":" What is m\u2220DEF?Enter your answer in the box. There is a triangle DEF in which side DE is congruent to side EF and G is the midpoint of the side DF. Segment EG intersect the side DF at point G. The measure of angle DEG is (3y+4) degrees and the measure of angle FEG is […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-150852","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/150852","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=150852"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/150852\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=150852"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=150852"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=150852"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
m\u2220DEG = m\u2220FEG
]<\/p>\n\n\n\n
m\u2220DEG = 3y + 4
]<\/p>\n\n\n\n
m\u2220FEG = 5y – 10
]<\/p>\n\n\n\n
3y + 4 = 5y – 10
]<\/p>\n\n\n\n\n
4 = 2y – 10
]<\/p>\n\n\n\n\n
14 = 2y
]<\/p>\n\n\n\n\n
y = 7
]<\/p>\n\n\n\n
m\u2220DEG = 3(7) + 4 = 21 + 4 = 25 \\text{ degrees}
]<\/p>\n\n\n\n
m\u2220FEG = 5(7) – 10 = 35 – 10 = 25 \\text{ degrees}
]<\/p>\n\n\n\n
m\u2220DEF + m\u2220DEG + m\u2220FEG = 180
]<\/p>\n\n\n\n
x + 25 + 25 = 180
]<\/p>\n\n\n\n
x + 50 = 180
]<\/p>\n\n\n\n
x = 130
]<\/p>\n\n\n\n
\\boxed{130 \\text{ degrees}}
]<\/p>\n\n\n\n