Question

please help me when you help me then god help you ok got it then thanks​

Answer 1

Given:

• ∠BAC = 75°
• ∠ABC = 65°
• ∠CDE = x
• ∠CED = 110°

To finD:

• Value of x

Solution:

In ∆ABC:

Given ∠BAC is 75°, ∠ABC is 65°. Let suppose that ∠ACB is a.

Now,

We know that according to Angle sum property of triangle, Sum of all interior angles of triangle is always equal to 180°. So we can say that ∠BAC + ∠ABC + ∠ACB is equal to 180°

Solving:

∠BAC + ∠ABC + ∠ACB = 180°

→ 75° + 65° + a = 180°

→ 140° + a = 180°

→ a = 180°-140°

→ a = 40°

Therefore,

∠ACB is 40°

_________________

Now, we know that vertically opposite angles are equal. So, in ∆ABC and in ∆CDE, ∠ACB and ∠DCE are vertically opposite angles.

Therefore,

∠ACB = ∠DCE = 40°

_________________

In ∆CDE:

Given that ∠DCE is 40°,∠CED is 110° and ∠CDE is x.

Now,

According to Angle sum property of triangle, we can say that ∠DCE +∠CED + ∠CDE equal to 180°.

Solving:

∠DCE +∠CED + ∠CDE = 180°

→ 40° + 110° + x = 180°

→ 150° + x = 180°

→ x = 180°-150°

→ x = 30°

Therefore,

$\huge{\boxed{\large{\mathfrak{\green{Value\:of\:x\:=\:\sf{30°}}}}}}$

$\huge{\bf{\blue{━━━━━ • ஜ • ❈ • ஜ • ━━━━━}}}$

Note: In your given picture, name of angles aren't visible properly so I also attached a picture with name of angles. If name of angles are wrong in my picture the kindly try to found it and correct.Focus on solution, if angles name are wrong then fix it. Thank you!