Question

Geometry

1). In the diagram below, DAE and FBCG are parallel lines. AC = BC and angle FBA = 130°.

a)calculate the vàlues of p,q,r, and t.​

Answer 1

Explanation:

∠FBA = 130°

∠FBA + p = 180 {Linear pair}

130 + p = 180

p = 180 - 130

p = 50°

AC = BC ⇒ r = p {angles opposite to equal sides are equal}

r = 50°

r + q = ∠FBA {external angle of a Δ equals sum of opposite internal angles}

50 +q = 130

q = 130 - 50

q = 80°

DE // FG , AC is transversal.

t = q {alternate interior angles}

t = 80°

DE // FG , AB is transversal.

s = p {alternate interior angles}

s = 50°