Question

Triangle Angle Sum Theorem

Answer 1

`\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}`

Given:

▪
`\longrightarrow \sf{KED = 100^\circ}`

▪
`\longrightarrow \sf{\angle ECD = 60^\circ}`

`\leadsto` According to the triangle angle sum theorem, the sum of interior angles of a triangle is 180°.

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

`\longrightarrow \sf{m \angle E+ m \angle K=180^\circ}`

`\longrightarrow \sf{m \angle E+ 100^\circ =180^\circ}`

`\longrightarrow \sf{m \angle E= 80^\circ}`

As we find the value of ∠E, we can replace it in the initial formula.
`\downarrow`

`\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}`

`\bm{m \angle C + m \angle \boxed{\bm D} = m \angle \boxed{\bm E}}`

`\bm{m \angle D= \boxed{\bm{ 40^\circ}}}`

Answer 2

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