In Fig., ∠ABC = 45° and ∠IKJ = 78°. Find angles ∠GEH, ∠HEF, ∠FED. Class 7

In Fig., ∠ABC = 45° and ∠IKJ = 78°. Find angles ∠GEH, ∠HEF, ∠FED. Class 7

Question 1.

In Fig., ∠ABC = 45° and ∠IKJ = 78°. Find angles ∠GEH, ∠HEF, ∠FED. Class 7

Solution:

∠BED = 45° (Corresponding angles)

So, ∠GEH = 45°. (Vertically opposite angles)

Also, ∠GEF = ∠IKE (Corresponding angles)

= 180° - 78° = 102°

So, ∠HEF = ∠GOF - ZGEH

= 102° - 45° = 57°.

Further, ∠FED = 180° - ∠GEF

= 180° - 102° = 78°.

Question 2.

In Fig.; AB is parallel to CD and CD is parallel to EF. Also, EA is perpendicular to AB. If ∠BEF = 55°, find the values of x and y. Class 7

Solution:

AB is parallel to CD and CD is parallel to EF.

So, AB is parallel to EF.

Therefore, x° + 55° = 180° (Interior angles on the same side of the transversal)

So, x = 180 - 55 = 125.

Also, CD is parallel to EF.

So, y° + 55° = 180° (Interior angles on the same side of the transversal)

Therefore, y = 180 - 55 = 125.