If m angle DEF = (6x+37) and mFGD = (19x-31), find m angle DEF

Question

asked Jan 14, 2021 217k views

2 Answers

Sebo · Answer 1 · 2021-01-19T08:36:42+0000

Answer:

$m \angle \ DE\ F = 127\°$

Explanation:

Given:

$m \angle \ DE\ F = (6x+37)$

$m \ arc \ FGD = (19-31)$

We need to find the m ∠ DEF.

Solution:

Now we can say that;

By inscribed angle theorem;

"The measure of the angle is twice the measure on the arc subtended by it."

so we get;

$2 \ m \angle DE\ F = m\ arc \ FGD$

2(6x+37)= 19x-31

Applying distributive property we get;

12x+74=19x-31

Combining the like terms we get;

$19x-12x=74+31\\\\7x = 105$

Dividing both side by 7 we get;

$(7x)/(7)=(105)/(7)\\\\x=15$

$m \angle \ DE\ F = (6x+37) = (6* 15+37) = 90+37 =127\°$

Hence
$m \angle \ DE\ F = 127\°$