Question

In a quadrilateral ABCD shown below it is known that BC is perpendicular to CD, angle A=3x+7, and angle C is 5x-15. given this information, which of the following a degree measure of angle A?(1) 40°(2) 55°(3) 70°(4) 82°

Answer 1

We know that

`BC\perp CD`

Wich means that

`\angle C=90`

We have an expression, in terms of x, for the values of angles A and C. Knowing the value of C, we just have to clear x from C's expression and replace it in A's:

`\begin{gathered} \angle C=5x-15\rightarrow90=5x-15\rightarrow105=5x\rightarrow x=(105)/(5)\rightarrow x=21 \\ \text{Thus, } \\ \angle A=3x+7\rightarrow\angle A=3(21)+7\rightarrow\angle A=63+7\rightarrow\angle A=70 \end{gathered}`

Hence, Angle A is worth 70°