Question

If in the figure a||b and c||d, then name the angles that are congruent to 2 ?

Answer 1

Step-by-step explanation:

Given that a∣∣b and c∣∣d

∠1=∠3 ...(i) (vertically opposite angles)

∠1=∠5 ...(ii) (a∣∣b, so, corresponding angles)

∠5=∠7 ...(iii) (vertically opposite angles)

From (ii) and (iii)

∠1=∠7 ...(iv)

∠1=∠9 ...(v) (c∣∣d,so,corresponding angles)

∠9=∠13 ...(vi) (a∣∣b,so,corresponding angles)

From (v) and (vi)

∠1=∠13 ...(vii)

∠9=∠11 ...(viii) (vertically opposite angles)

From (v) and (viii)

∠1=∠11 ...(ix)

∠13=∠15 ...(x) (vertically opposite angles)

From (vii) and (x)

∠1=∠15 ...(xi)

From (i),(ii),(iv),(v),(vii),(ix),(xi)

∠1=∠3=∠5=∠7=∠9=∠11=∠13=∠15