Question

Equation with angles can someone please answer help please

Answer 1

∠A = 166°

Explanation:

We can imagine the parallel line to the left as a shifted version of the one on the right. As we move it further left along the line the in middle (called a transversal), ∠B will slide closer and closer to ∠A. Eventually, the two will totally coincide, showing that ∠B ≅ ∠A. We call ∠A and ∠B corresponding angles, because they can be made to perfectly overlap in that way.

Since corresponding angles are congruent, their measures must be equal, so in this example, we can say that

`\angle A =\angle B`, and since
`\angle A = 7x+40^(\circ)` and
`\angle B=3x+112^(\circ)`,

`7x+40^(\circ)=3x+112^(\circ)`

To solve for x, we can subtract 3x and 40° from both sides:

`4x=72^(\circ)`

and divide both sides by 4:

`x=18^(\circ)`

We can now replace x with 18° in our expression for ∠A to find

`\angle A = 7(18^(\circ))+40^(\circ)\\\angle A=126^(\circ)+40^(\circ)\\\angle A=166^(\circ)`