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lisov135 [29]
3 years ago
8

Given EFGH and E=45°, what is the measure of angle F?

Mathematics
2 answers:
Ivahew [28]3 years ago
4 0
Opposite angles are congruent and adjacent angles are supplementary.

so < E + < F = 180...and < E = 45
45 + < F = 180
< F = 180 - 45
< F = 135 <==
Goryan [66]3 years ago
3 0
Remember that opposite angles are congruent. 

So,

we know that <E= <G

That is 45+45= 90 degrees 

We also know that consecutive angles are supplementary. E and F would equal 180 degrees. 

180-45=135

<F= 135 degrees. 

We can check this by seeing if all the angles add up to 360 degrees/

135+135+45+45

=360 <== this works

I hope this helps!
~kaikers
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lawyer [7]

Answer:

m∠U = 103° and m∠TRS = 6°

Step-by-step explanation:

In the given circle O,

Since, RS║VU, and VR is a transverse,

Therefor, m∠V + m∠R = 180° [Consecutive interior angles]

m∠R + 103° = 180° [m∠R = 103° given]

m∠R = 180° - 103°

m∠R = 77°

Since m∠R = m∠VRT + m∠TRS

77° = 71° + m∠TRS

m∠TRS = 77° - 71° = 6°

Quadrilateral RTUV is a cyclic quadrilateral.

Therefore, m∠U + m∠R = 180°

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m∠U = 180° - 77° = 103°

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