In the adjoining figure, it is given that CE || BA, =80^ and =35^ . Find 1. , 2. , 3. .

Given: CE || BA =80^ , =35^ 1. = =80^ (alternate angles with AC as a transversal) 2. + =180^ (linear pair) + + =180^ + 80^ +35^ =80^ + 65^ 3. In : + + =180^ (angle sum property) 80^ +65^ + =180^ + 35^

In the adjoining figure, it is given that CE || BA, =80^ and =35^…

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Question

In the adjoining figure, it is given that $\text{CE || BA},\ \angle\text{BAC}=80^\circ$ and $\angle\text{ECD}=35^\circ.$ Find

$\angle\text{ACF},$
$\angle\text{ACB},$
$\angle\text{ACF}.$

✓

Answer

Given: $\text{CE || BA}$
$\angle\text{BAC}=80^\circ,\ \angle\text{ECD}=35^\circ$

$\angle\text{BAC}= \angle\text{ACE}=80^\circ$ (alternate angles with AC as a transversal)
$\angle\text{ACB}+ \angle\text{ACD}=180^\circ$ (linear pair)

$\angle\text{ACB}+ \angle\text{ACE}+\angle\text{ECD}=180^\circ$
$\angle\text{ACB}+ 80^\circ+35^\circ=80^\circ$
$\angle\text{ACB}+ 65^\circ$

$\text{In}\ \triangle\text{ABC}:$

$\angle\text{BAC}+ \angle\text{ACB}+\angle\text{ABC}=180^\circ$ (angle sum property)
$80^\circ+65^\circ+\angle\text{ABC}=180^\circ$
$\angle\text{ABC}+ 35^\circ$

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