Question

17. In the given figure, ABI/CD. 3 points
If angle CAB=80° and angle
EFC=25°, then angle CEF=?
250
800
8​

Answer 1

Given :-

AB || CD

∠CAB = 80°

∠EFC = 25°

Required to find :-

Measure of the ∠CEF ?

Concept used :-

▶ The sum of two interior angles on the same side of the transversal is supplementary .

▶ Vertically Opposite angles are equal

▶ The sum of all angles in a triangle will add up to 180°

▶ This is also known as " Angle Sum Property " .

Solution :-

Given that :-

AB || CD

∠CAB = 80° & ∠EFC = 25°

we need to find the measurement of ∠CEF

So,

Let's consider ;

AB || CD , AC is the transversal

So,

From the diagram we can conclude that ;

∠CAB + ∠ACD = 180°

[ Reason : Interior angles on the same side of the transversal ]

80° + ∠ACD = 180°

∠ACD = 180° - 80°

∠ACD = 100°

Hence,

∠ACD = 100°

However,

We can also conclude that ;

∠ACD = ∠ECF

[ Reason : Vertically Opposite Angles ]

So,

∠ECF = 100°

Now,

Let's consider ∆ECF

In ∆ECF ,

∠EFC + ∠ECF + ∠CEF = 180°

[ Reason :- Angles Sum Property ]

25° + 100° + ∠CEF = 180°

125° + ∠CEF = 180°

∠CEF = 180° - 125°

∠CEF = 55°

Therefore,

∠CEF = 55°

Hence,