Easy 20 points. i am have a time limit and i am stuck on this one part. simple answers are okay just quickly.

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Step-by-step explanation:

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Step-by-step explanation:

2. Conclusion: U is the mid point of RN.

Justification: From the figure, you can see that RU=UN which means U divides the line segment RN in two equal halves, thus by definition of mid point theorem, U is the mid point of RN.

3. From the given figure,

Conclusion: ∠7=∠5

Justification: From the figure, you can see that \overrightarrow{IK} bisects∠MIE. Therefore by the definition of bisector angle property, ∠MIK=∠KIE that is ∠7=∠5.

4. Conclusion: if l║m, and t is the transversal, then ∠3=∠7.

Justification: Since l║m and t is the transversal, then ∠3=∠7 as the alternate angles made by the transversal are equal.

5. Conclusion:    If \overrightarrow{BD} bisects ∠ABC, then ∠ABD=∠DBC

Justification: Since,  \overrightarrow{BD} bisects ∠ABC, then by the bisector angle property,  \overrightarrow{BD} divides ∠ABC in two equal angles that is ∠ABD=∠DBC.

6. Conclusion: If ∠2+∠3= 180°,then ∠2 and ∠3 are supplementary angle pairs.

Justification: Since, ∠2 and ∠3 are supplementary angle pairs which are on the same side of the transversal t, their sum is equal to 180° that is ∠2+∠3= 180°.

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°