Question

In the adjacent figure, it is given that, BC || DE, ∠BAC=35° and ∠BCE=102°. Find the measure of (i) ∠ BCA (ii) ∠ADE and (iii) ∠CED.

Answer 1

Answer:  1) 78°, 2) 67°, 3) 78°

Step-by-step explanation:

Since we have given that

BC || DE, ∠BAC=35° and ∠BCE=102°.

So, we need to find the measure of (i) ∠ BCA (ii) ∠ADE and (iii) ∠CED.

1) Since ∠BCE and ∠ BCA are linear pair.

So, it becomes,

$102^\circ+\angle BCA=180^\circ\\\\\angle BCA=180^\circ-102^\circ\\\\\angle BCA=78^\circ$

2) ∠ADE.

In ΔABC, we have

$\angle A+\angle B+\angle C=180^\circ\\\\35^\circ+\angle B+78^\circ=180^\circ\\\\\angle B+113^\circ=180^\circ\\\\\angle B=180^\circ-113^\circ\\\\\angle B=67^\circ$

So, ∠ADE and ∠ABC are corresponding angles and so they are equal.

so, ∠ADE = 67°

3) ∠CED.

$\angle CED=\angle ACB=78^\circ$

Hence, 1) 78°, 2) 67°, 3) 78°

Answer 2

Step-by-step explanation:

This solution is right

Explanation is there in photo.