Question

12. Quadrilateral ABCD is congruent to quadrilateral EFGH. If mZA = 6x - 8 and mZE = 4x + 1, find m2A. Choose: © 19° O 24° O 40° 0 51°

Answer 1

Let's draw the figures to better understand the scenario:

The figure appears that ∠A and ∠E are pairs of corresponding angles. Since it was given that the two quadrilaterals are congruent, ∠A and ∠E must also be congruent.

With this relationship, let's first determine the value of x to be able to determine the measure of ∠A.

We get,

`\text{ 6x - 8 = 4x + 1}`
`\text{ 6x - 8 + 8 - 4x = 4x + 1 + 8 - 4x}`
`\text{ 6x - 4x = 1 + 8}`
`\text{ 2x = 9}`
`\text{ }\frac{\text{2x}}{2}\text{ = }\frac{\text{9}}{2}`
`\text{ x = }(9)/(2)`

Let's determine the measure of ∠A.

`\text{ }\angle A\text{ = 6x - 8 = 6(}(9)/(2))\text{ - 8}`
`\text{ = 3(9) - 8}`
`\text{ = 27 - 8}`
`\text{ }\angle A=19^(\circ)`

Therefore, the measure of ∠A is 19°. The answer is letter A or the 1st option.