Question

In the following figure, D and E are points on sides AB and AC of ∆ ABC respectively such that DE || BC. If angle B = 30° and angle A = 40°, find x,y and z.​

Answer 1

Step-by-step explanation:

In triangle ABC

line DE || line BC and line AB is the transversal

m/ DBC=m/ ADE (corresponding angles)

m/ ADE=30 degree

m/ x=30degree

In triangle ADE

m/ ADE +m/ AED +m/ EAD =180 degree .... (sum of all angles of a triangle)

m/ x +m/ z+40 =180

30+m/ z+40 =180

70+m/ z =180

m/ z =180-70

m/ z =110degree

line DE || line BC and line AC is the transversal

m/ AED =m/ ECB (corresponding angles)

m/ z=m/ y

m/ y=110degree