In the adjacent figure, it is given that, BC || DE, ∠BAC=35° and �

1.	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» 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°

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»

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

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