Question

Q. 3. Solve the following. (Any two) (06) 1) Prove that the opposite angles formed by two intersecting lines are of equal 002 P NON measures. ii) Prove that the sum of measures of all angles of a triangles is 180 iii) In fig. line AB line CD and line PO is transversal. Measure of one of the angle is given R Find the measures of the following: А 105" B a) ZART b) ACTQ c) ZDTQ 'T D Q​

Answer 1

Answer: 1

Given:-

Line AB and line CD intersect at point O

To prove:-

<AOD=<DOB

<DOB=<BOC

PROOF:

Line AB and line CD have common arm as OD and OB..

Therefore, <AOD+<DOB=180°

Therefore, <DOB+<BOC=180°

<AOD+<DOB=<DOB+<BOC [<DOB, DOB will cut out]

Therefore, <AOD=<BOC

Similarly <DOB=<AOC

______________________

Answer 2:

Given:-

Triangle ABC

To Prove:-

<A+<B+<C=180°

Proof:

Draw a line xy parallel to BC

Now, <X+<A+<Y=180°

Therefore, <4+<1+<5=180°

Therefore, <1+<2+<3=180°

Therefore, <A+<B+<C=180°

Hence proved //