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

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2 votes

Answer: 127

Explanation:

User Jeff Lewis
by
8.1k points
2 votes

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\°

User Sebo
by
8.6k points

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