Question

In the given figure, AB || FC, ∠B = 70° and ∠FDE = 148°. Find the values of a and b.

Answer 1

Given:

AB || FC

∠B = 70°

∠FDE = 148°

Find a and b likely angles in the figure.

Step 1: Analyze the figure

Since AB || FC, we can use the properties of parallel lines and alternate interior angles.

Let’s assume a = ∠BDE or a similar angle formed by a transversal crossing parallel lines.

Let’s assume b = ∠DFC (or another angle related by triangle angle sum).

We are given:

∠B = 70°

∠FDE = 148° → This is a straight angle minus internal angle.

Step 2: Use supplementary angles

At point D, we have:

∠FDE + ∠BDE = 180°

148 + a = 180°

a = 32°

Step 3: Use triangle angle sum

In triangle BDE, sum of angles = 180°

Let’s denote: ∠BDE = a, ∠DBE = b, ∠B = 70°

Also, at point D, ∠FDE = 148° → Remaining angle = 180 – 148 = 32°

So triangle BDE: angles: 70°, 32°, a

70 + 32 + a = 180°

a = 78°

Step 4: Find b

Since AB || FC, angle ∠B and angle b are co-interior angles:

∠B + ∠b = 180°

70 + b = 180°

b = 110°