Question

Angle a and angle C are opposite angles so angle a is congruent to angle c 8b equals 112 b equals 14

Answer 1

We know that

`\angle A\cong\angle C`

So,

`\angle A\cong\angle C\text{ }\rightarrow\text{ 8b=112 }\rightarrow\text{ b=112/8 }\rightarrow\text{ b=}14`

Because we are working with a quadrilateral, we also know that

`\angle A+\angle B+\angle C+\angle D=360`

But we already know that

`\angle A=\angle C=112`

And since we have two equal angles in a quadrilateral, we have no other option but for the remaining 2 angles to be equal. That means that

`AB=CD\text{ }\rightarrow\text{ 2a=34 }\rightarrow\text{ a=34/2 }\rightarrow\text{ a=17}`

Hence,

`a=17\text{ , b=14}`