Question

If angle 1=75 then find the measurements of angle 2,3,6,7,8

Answer 1

Answer:

2=105

3=75

4=105

5=75

6=105

7=105

8=75

Step-by-step explanation:

very easy and interesting question

Answer 2

Answer

• ∠2 = 105°
• ∠3 = 75°
• ∠6 = 105°
• ∠7 = 105°
• ∠8 = 95°

Explanation

Given

✭ ∠1 = 75°

To Find

◈ The value of,

• ∠2
• ∠3
• ∠6
• ∠7
• ∠8

Solution

So here we see that the two lines G & H are parallel to each other so which means we may have a lot of combinations as follows,

• Internal opposite angles are equal
• External opposite angles are equal
• Adjacent angles add up to 180°
• Co-interior angles add up to 180°
• Vertically Opposite Angles are equal

[From these rules we may derive the needed values]

Finding ∠2

➝ ∠1 + ∠2 = 180°

[Adjacent angles]

➝ 75° + ∠2 = 180°

➝ ∠2 = 180° - 75

➝ ∠2 = 105°

Finding ∠3

➝ ∠1 = ∠3

[Vertically Opposite]

➝ ∠3 = 75°

Finding ∠6

➝ ∠3 + ∠6 = 180°

[Co-interior angle]

➝ 75° + ∠6 = 180°

➝ ∠6 = 180°-75°

➝ ∠6 = 105°

Finding ∠7

➝ ∠6 = ∠7

[Vertically Opposite]

➝ ∠7 = 105°

Finding ∠8

➝ ∠6 + ∠8 = 180°

[Linear Pair]

➝ 105° + ∠8 = 180°

➝ ∠8 = 180°-105°

➝ ∠8 = 95°