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Sloan [31]
2 years ago
12

If mZGEF is thirteen less than five times mZDEG and mZDEF = 149°, find mZGEF. F D G

Mathematics
1 answer:
Goryan [66]2 years ago
4 0

Answer:

Step-by-step explanation:

Given :

From the diagram,

m∠GEF is 13 less than 5 times m∠DEG and ∠DEF = 149°,.

To Find :

the value of m∠GEF..

Solution :

As per given data,

m∠GEF = 5m∠DEG - 13° ...(i)

∠DEF = 149° ⇒ m∠GEF + m∠DEG = 149° ..(ii)

Substituting value of m∠GEF in (ii),

We get,

(5m∠DEG - 13°) + m∠DEG = 149°

6m∠DEG - 13° = 149°

6m∠DEG = 149° + 13° = 162°

m∠DEG = ° = 27°

Substituting value of m∠DEG in (i),

We get,

m∠GEF = 5(27°) - 13°

m∠GEF = 135° - 13°= 122°

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√180 can be expressed in the form p√q. where p and q are integers. Find the smallest value of p + q. ​
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Answer:  

The smallest value of p+q is 11

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=======================================================

Explanation:

Let's factor 180 in such a way that exactly one factor is a perfect square.

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Here are the possible factorizations we could go with:

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Those factorizations then lead to the following

\sqrt{180} = \sqrt{4*45} = \sqrt{4}*\sqrt{45}= 2\sqrt{45}\\\\\sqrt{180} = \sqrt{9*20} = \sqrt{9}*\sqrt{20}= 3\sqrt{20}\\\\\sqrt{180} = \sqrt{36*5} = \sqrt{36}*\sqrt{5}= 6\sqrt{5}\\\\

Then we have

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