Question

find the lettered angle in each case

Answer 1

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(iii) • <x = 70○ (vertically opposite angles)

• <z = 180○-110○ = 70○ (linear pair)

<x + <y + <z = 180○ (angle sum ppty)
70○+ <y + 70○ =
140○ + <y = 180○

• <y = 180○-140○ = 40○

(iv) <AEF = 180○-100○ = 80○

<A + <AEF + <AFE = 180○ (angle sum ppty)
= 50○ + 80○ + <AFE = 180○
= 130○ + <AFE = 180○
<AFE = 180○-130○ = 50○

<DFB = 50○ (vertically opposite angles.)

<DBF = 180○-90○ (linear pair) = 90○

<DFB + <DBF + <z = 180○ (linear pair)
50○ + 90○ + <x = 180○
140○ + <x = 180○
<x = 180○ - 140○

• <x = 40○

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