Answered

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Triangle Angle Sum Theorem

Triangle Angle Sum Theorem class=

Sagot :

jcherry99

Answer:

Step-by-step explanation:

Comment

The sum of the remote interior angles = The exterior angle not connected to them

What that means is that

<C + <D = <KEB

Givens

<C = 60

<KED = <C + <D

Solution and answer

<KED = <C + <D                      Substitute the givens into this equation

100 = 60 + <D                         Turn this around

<60 + <D = <100                     Answer first equation

Subtract 60 from both sides

<60-<60 + <D = <100 - 60

<D = <40                                   Answer second Equation

Kailes

[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

Given:

▪ [tex]\longrightarrow \sf{KED = 100^\circ}[/tex]

▪ [tex]\longrightarrow \sf{\angle ECD = 60^\circ}[/tex]

[tex]\leadsto[/tex] According to the triangle angle sum theorem, the sum of interior angles of a triangle is 180°.

[tex]\leadsto[/tex] We can find the value of ∠E if we know the sum of two supplementary angles is equal to 180°

[tex]\longrightarrow \sf{m \angle E+ m \angle K=180^\circ}[/tex]

[tex]\longrightarrow \sf{m \angle E+ 100^\circ =180^\circ}[/tex]

[tex]\longrightarrow \sf{m \angle E= 80^\circ}[/tex]

As we find the value of ∠E, we can replace it in the initial formula. [tex]\downarrow[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

[tex]\bm{m \angle C + m \angle \boxed{\bm D} = m \angle \boxed{\bm E}}[/tex]

[tex]\bm{m \angle D= \boxed{\bm{ 40^\circ}}}[/tex]

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