Question

Find the measure of the angle indicated in bold. #5

Answer 1

The measure of angle BCO, formed by the intersection of line XY with parallel lines AB, PQ, and ST, is 90 degrees. This is deduced by equating corresponding angles BCO and COP and solving for x.

Certainly! Since line XY intersects three parallel lines (AB, PQ, and ST), creating corresponding points of intersection C, O, and U, we can use the properties of parallel lines and transversals.

The angles BCO and COP are corresponding angles formed by the transversal XY intersecting the parallel lines AB and PQ. According to the properties of corresponding angles, these angles are congruent.

So, we can set up an equation:

`\[ \text{Angle BCO} = \text{Angle COP} \]`

16x - 6 = 15x

Now, solve for x:

x = 6

Now that we have the value of x, substitute it back into the expression for angle BCO:

`\[ \text{Angle BCO} = 16x - 6 \]`

`\[ \text{Angle BCO} = 16(6) - 6 \]`

`\[ \text{Angle BCO} = 90 \]`

Therefore, the measure of angle BCO is 90 degrees.

Answer 2

90°

Explanation:

16x - 6 and 15x are alternate angles and are congruent, then

16x - 6 = 15x ( subtract 15x from both sides )

x - 6 = 0 ( add 6 to both sides )

x = 6

Then

16x - 6 = 16(6) - 6 = 96 - 6 = 90°