∠ KGH is equal to 77°. This is arrived at by using the knowledge of the total angles in Parallel Lines.
What are the total angles on a straight line?
According to the laws of lines and angles, the total number of angles that can exist on a straight line is 180°.
If ∠CED = 25° and ∠BFL = 78°, then: ∠KGH = 180-(25+78), which is equals 77°. This is because the total angles on a straight-line total 180°
What is ∠LKJ?
Recall that in angles in parallel lines:
- Corresponding Angles are always congruent,
- Alternate Angles are always congruent, and
- Interior According always sum up to 180°
Hence,
We can derive ∠LKJ because it is congruent with ∠BGJ.
To get ∠BGJ, we must get ∠LFH because both of them are interior angles and sum up to 180°.
To get ∠LFH, we must subtract ∠BFL from 180° because they are both angles on a straight line.
Hence ∠LFH = 180 - 78 = 102°
Recall that ∠LFH and ∠BGJ are interior angels. Hence
∠BGJ = 180 - 102 = 78°.
Since ∠BGJ is a corresponding ∠ with ∠LKJ, therefore
∠LKJ = 78°
What is ∠ALM?
∠ALM is ∠BFL because they are both corresponding angles and are therefore congruent.
What are the solutions to section B?
- Because ∠ACB and ∠BAC are equal, therefore sides AB and BC are equal in length. We can tell that ∠ACB and ∠BAC are equal because the total angles in the triangle are equal to 180°
2. The name given to the triangle mentioned above is Obtuse
Triangle. This is because one of the angles exceeds 90°.
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