Question

In Triangle DEF, the sum of the measures of Angle D and Angle E is 110. The sum of the measures of Angle E and Angle F is 150. Find the sum of the measures of Angle D and F.​

Answer 1

Answer:

<D + <F = $100^{o}$

Step-by-step explanation:

Given: <D + <E = $110^{o}$

           <E + <F = $150^{o}$

But, the sum of angles in a triangle = $180^{o}$.

Thus;

<D + <E + <F = $180^{o}$

$110^{o}$ + <F = $180^{o}$

⇒ <F = $180^{o}$ - $110^{o}$

        = $70^{o}$

<F = $70^{o}$

Also,

<E + <F = $150^{o}$

<E + $70^{o}$ = $150^{o}$

<E = $150^{o}$ - $70^{o}$

    = $80^{o}$

<E = $80^{o}$

So that;

<D + <E = $110^{o}$

<D + $80^{o}$ = $110^{o}$

<D = $110^{o}$ - $80^{o}$

     = $30^{o}$

<D = $30^{o}$

⇒ <D = $30^{o}$, <E = $80^{o}$, and <F = $70^{o}$.

Therefore;

<D + <F = $30^{o}$ + $70^{o}$

             = $100^{o}$