Question
Find 
and 
.
Hint:
We are given three intersecting lines. HF, DE and GE are the given lines. Line HF and DE intersect each other at point E. They are perpendicular to each other. Line GE intersects like HF at point E making some angle with it. We are asked to find the angles between the pair of lines GE,DE and HF,GE. We will use the properties of intersecting lines.
The correct answer is:
The given lines are HF, DE and GE.
The given angles are as follows:
∠DEH = 90°
∠DEG = 6x°
∠GEF = 4x°
The angles ∠DEH and ∠DEF are supplementary angles. Supplementary angles are the angles that form a line. Their sum is 180°.
So,
∠DEH + ∠DEF = 180°
90° + ∠DEF = 180°
∠DEF = 180° - 90°
∠DEF = 90°
From the figure we can see that, the angles ∠DEG and ∠GEF add up to form ∠DEF.
∠DEG + ∠GEF = ∠DEF
6x° + 4x° = 90°
10x° = 90°
x = 9
Now, we will substitute the value “x” in the equations of the angles.
∠DEG = 6x°
= 6 × 9
∠DEG = 54°
∠GEF = 4x°
= 4 × 9
∠GEF = 36°
The values of the angles are ∠DEG = 54° and ∠GEF = 36°.
For such questions, we should know about supplementary angles. We should know about the properties of intersecting lines. We have to be careful about the point of interaction of lines.
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