Question

if AB||CD and CD||EF, find ACE​

Answer 1

• ∠ACE is of 20°.

Step-by-step explanation:

Given:-

• AB || CD.
• CD || EF .

To find

• Measure of ∠ACE.

Construction:-

• Draw a line CM which will parallel to AB.

Solution:-

Sum of two angles on the same side of the transversal in a figure where two parallel lines are intersected by transversal is 180°. This property is also known as Co-interior angle.

So,

➝ ∠CEF + ∠ECD = 180°

➝ 130° + ∠ECD = 180°

➝ ∠ECD = 180° - 130°

➝ ∠ECD = 50°

Similarly,

➝ ∠BAC + ∠ACM = 180°

➝ 70° + ∠ACM = 180°

➝ ∠ACM = 180° - 70°

➝ ∠ACM = 110°

We also know that,

Sum of all angles forms on straight line is equal to 180°. This statement is also known as linear pair.

So,

➝ ∠ACM + ∠ECD + ∠ACE = 180°

➝ 110° + 50° + ∠ACE = 180°

➝ 160° + ∠ACE = 180°

➝ ∠ACE = 180° - 160°

➝ ∠ACE = 20°

Therefore,

∠ACE is of 20°.

Answer 2

GIVEN:-

• AB || CD, CD || EF

TO FIND:-

• Measure of ∠ACE

SOLUTION:-

As per the diagram, lines CD ∣∣ EF and CE is transveral.

As we know,

The sum of interior angles is equal to 180°

⇒ ∠ECD + ∠CEF = 18O°

⇒ ∠ECD + 130° = 180°

⇒ ∠ECD = 180 − 130°

⇒ ∠ECD = 50°

As per the diagram, lines AB ∣∣ CD and CA is transveral.

We know that alternate angles are equal.

→ ∠BAC = ∠ACD

→ ∠BAC = ∠ACE + ∠ECD

→ 70° = ∠ACE + 50°

→ 20° = ∠ACE

∴∠ACE = 20°

Hence,

• ∠ACE = 20°