Question

Find the values of x and y in the diagram below

Answer 1

• Vertical Angles: Non-adjacent angles formed when two lines intersect. They are congruent (equal to each other).
• Linear Pair: Adjacent angles formed when two lines intersect. They are supplementary (add up to 180).

Firstly, since (2x + 1) and (x + 26) are vertical angles, we can solve them as such:

$2x+1=x+26\\x+1=26\\x=25$

Next, add 25 to 26 to get the (x + 26) value:

$25+26=51$

51° and (3y - 60) are a linear pair. Using this info, we can solve for it as such:

$3y-60+51=180\\3y-9=180\\3y=189\\y=63$

In short, x = 25 and y = 63.