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in the adjoining figure ,ifAB || CD ,∆ A=50°and ∆B=40°, find the measures of the remaining four angles give reasons for your answer
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in the adjoining figure ,ifAB || CD ,∆ A=50°and ∆B=40°, find the measu...
first angel is 130
and second angel is 140
This question is part of UPSC exam. View all Class 7 courses
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in the adjoining figure ,ifAB || CD ,∆ A=50°and ∆B=40°, find the measu...
Understanding Angles in Parallel Lines
When two lines are parallel, several angle relationships come into play. Given that AB || CD, we can use the properties of alternate interior angles and corresponding angles to find the remaining angles in the triangle.
Given Information
- Angle A = 50°
- Angle B = 40°
Step 1: Finding Angle C
- Since AB || CD, angle A and angle C are corresponding angles.
- Therefore, Angle C = Angle A = 50°.
Step 2: Finding Angle D
- Again, since AB || CD, angle B and angle D are corresponding angles.
- Hence, Angle D = Angle B = 40°.
Step 3: Finding Angle E
- In triangle ABC, the sum of the angles is always 180°.
- We already have angles A and B. So, we can calculate angle E as follows:
Angle E = 180° - (Angle A + Angle B)
Angle E = 180° - (50° + 40°)
Angle E = 180° - 90°
Angle E = 90°.
Step 4: Finding Angle F
- In triangle BCD, we can also apply the sum of angles property:
Angle F = 180° - (Angle C + Angle D)
Angle F = 180° - (50° + 40°)
Angle F = 180° - 90°
Angle F = 90°.
Summary of Angles
- Angle A = 50°
- Angle B = 40°
- Angle C = 50°
- Angle D = 40°
- Angle E = 90°
- Angle F = 90°
This systematic approach using parallel lines and triangle properties allows us to accurately determine all the angles in the given geometric configuration.
When two lines are parallel, several angle relationships come into play. Given that AB || CD, we can use the properties of alternate interior angles and corresponding angles to find the remaining angles in the triangle.
Given Information
- Angle A = 50°
- Angle B = 40°
Step 1: Finding Angle C
- Since AB || CD, angle A and angle C are corresponding angles.
- Therefore, Angle C = Angle A = 50°.
Step 2: Finding Angle D
- Again, since AB || CD, angle B and angle D are corresponding angles.
- Hence, Angle D = Angle B = 40°.
Step 3: Finding Angle E
- In triangle ABC, the sum of the angles is always 180°.
- We already have angles A and B. So, we can calculate angle E as follows:
Angle E = 180° - (Angle A + Angle B)
Angle E = 180° - (50° + 40°)
Angle E = 180° - 90°
Angle E = 90°.
Step 4: Finding Angle F
- In triangle BCD, we can also apply the sum of angles property:
Angle F = 180° - (Angle C + Angle D)
Angle F = 180° - (50° + 40°)
Angle F = 180° - 90°
Angle F = 90°.
Summary of Angles
- Angle A = 50°
- Angle B = 40°
- Angle C = 50°
- Angle D = 40°
- Angle E = 90°
- Angle F = 90°
This systematic approach using parallel lines and triangle properties allows us to accurately determine all the angles in the given geometric configuration.
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in the adjoining figure ,ifAB || CD ,∆ A=50°and ∆B=40°, find the measures of the remaining four angles give reasons for your answer Related: NCERT Solutions Chapter 6 (Part - 1) - The Triangle and Its Properties, Maths, Class 7
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