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 |
In step 1, we have:
\widehat{b} =\widehat{c}
If we use the fact that \widehat{d} and \widehat{c} are supplementary as seen in step 2, then we can find the measure of \widehat{c} in step 3.
In step 4, we apply steps 1 and 3 to conclude that \widehat{b}=60^\circ.
Step 2 : \widehat{c} and \widehat{d} are supplementary.
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 |
Corresponding angles are congruent. We use this fact to conclude that \widehat{CBA} = 50^\circ and \widehat{BCA}=30^\circ
Corresponding angles are congruent hence \widehat{CBA} = 50^\circ and \widehat{BCA}=30^\circ
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 |
In step 1, we find \sin\left(\widehat{BAC}\right). So in Step 2, we conclude that:
\widehat{BAC} = 30^\circ
Use this and step 3 to determine b.
Step 2 : \widehat{BAC} = 30^\circ
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 |
We need to find \widehat{BAC} in step 2 to conclude that \widehat{BAC}=60^\circ
\widehat{BAC} and the 30 degree angle are vertical angles, so \widehat{BAC}=30^\circ.
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 |
In Step 3 we have \widehat{a} = 60^\circ. We need a reasoning for this in step 2.
\widehat{CBA} and \widehat{E}_1 are corresponding angles so they are congruent
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 |
We know that the alternate exterior angles are congruent. Hence:
\widehat{BCA}=50^\circ
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 |
In step 1, \widehat{B} and \widehat{AED} are corresponding angles. We know that corresponding angles are congruent. Therefore:
\widehat{EDA}=30^\circ