Question

q1 - accelerated mathematics gr 8 | lesson: transversals and parallel lines: solving unknown...
target due: last friday 0%
corresponding angles are:
a. never equal
b. always different
c. sometimes equal
d. always equal
what is the value of a if ∠4 = 3a + 40 and ∠5 = 2a + 50 are consecutive interior angles?
a. 18
b. 22
c. 14
d. 10

Explanation:

Step1: Recall corresponding - angles property

When a transversal intersects two parallel lines, corresponding angles are always equal.

Step2: Recall consecutive - interior angles property

Consecutive interior angles are supplementary when a transversal intersects two parallel lines. So, \(\angle4+\angle5 = 180\).

Step3: Substitute angle expressions

Substitute \(\angle4 = 3a + 40\) and \(\angle5=2a + 50\) into the equation \(\angle4+\angle5 = 180\). We get \((3a + 40)+(2a + 50)=180\).

Step4: Simplify the left - hand side

Combine like terms: \(3a+2a+40 + 50=180\), which simplifies to \(5a+90 = 180\).

Step5: Solve for \(a\)

Subtract 90 from both sides: \(5a=180 - 90\), so \(5a = 90\). Then divide both sides by 5: \(a=\frac{90}{5}=18\).

Answer:

1. d. Always equal
2. d. 10