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Complete proofs involving angles Geometry

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Find the missing step in the following reasoning in order to show that \widehat{b}=60^\circ, given that the horizontal lines are parallel.

1

\widehat{b} and \widehat{c} are corresponding angles so \widehat{b}=\widehat{c}

2

...
3 \widehat{c} = 180^\circ - 120^\circ = 60^\circ
4 \widehat{b}=60^\circ
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Find the missing step in the following reasoning in order to determine \widehat{a}, given that the horizontal lines are parallel.

1

\widehat{CBA} and a 50 degree angle are corresponding angles.
2

\widehat{BCA} and a 30 degree angle are corresponding angles.
3 ................
4 \widehat{a}=180^\circ-\left( \widehat{BCA} + \widehat{ABC}\right) = 180^\circ-\left(30^\circ + 50^\circ\right)=100^\circ
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Find the missing step in the following reasoning in order to show that b=150^\circ.

1

\sin\left(\widehat{BAC}\right)=\dfrac{2}{4}= \dfrac{1}{2}

2

.....
3 \widehat{a} and \widehat{b} are supplementary angles.
4 \widehat{b}=150^\circ
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Find the missing step in the following reasoning in order to show that \widehat{BCA}=60^\circ.

1

\widehat{BCA}+ \widehat{BAC}+90^\circ=180^\circ

2

.....
3 \widehat{BCA}= 180^\circ-\left(90^\circ+30^\circ\right)=60^\circ
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Find the missing step in the following reasoning in order to show that \widehat{b}=120^\circ, given that the horizontal lines are parallel.

1

\widehat{CBA}= 180^\circ - \left(90^\circ+ 30^\circ\right)=60^\circ

2

...
3 \widehat{a}=60^\circ
4 \widehat{b}=180^\circ -60^\circ=120^\circ
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Find the missing step in the following reasoning in order to determine \widehat{A}, given that the horizontal lines are parallel.

1

\widehat{BCA} and the 50 degree angle are alternate exterior angles.
2 .....
3

\widehat{ABC} and the 120 degree angle are supplementary,
3 \widehat{ABC}=60^\circ
4 \widehat{A}=180^\circ-\left(60^\circ + 50^\circ\right)=70^\circ
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Find the missing step in the following reasoning in order to show that \widehat{A}=20^\circ, given that the horizontal lines are parallel.

1

\widehat{B} and \widehat{EDA} are corresponding angles.
2

...
3 \widehat{AED} and the 50 degree angle are supplementary.
4 \widehat{AED}=130^\circ
5 \widehat{A}=180^\circ-\left(130^\circ+30^\circ\right)=20^\circ