Determine all the missing angle . Justify your answers andshow your work

1 Answer

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llltkl | College Teacher | (Level 3) Valedictorian

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Given that line segment AD ll CL, AL is a transversal,

`angle DAL=angle ALC ` (alternate interior angles are congruent)`=33^o`

Now consider `Delta ALC, angle CAL=180^o-(33+53+40)=54^o`

Again consider `Delta AXC, angle AXC=180^o-(54+40)=86^o`

Opposite `angle DXL=angle AXC=86^o`

`angleCXL=opposite angleAXD=(180-86)=94^o`

From `Delta LDC, angle LDC=180-(53+33+21)=73^o`

Finally, `from Delta ADC, angle ADC=180-(54+33+40)=53^o`