Title Discovering Geometry through Problem Solving Form

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guys this looks like a fun one we're giving some triangles with some angles this is congruent to this and they give us the values of these two angles and they're asking us to solve for x let's do this if you want to try this on your own pause it because I'm going to solve it in three two one for the first step let's focus on this linear pair right here I want to find out what is this other angle combine these form 180 degrees so we know that the question mark plus 45 will equal 180. that'll be true if the question mark is 135 so we know that this angle is 135 degrees next let's focus on this triangle right here what is the value of this angle the sum of the interior angles of a triangle is always equal to 180 degrees and this will be true for 30 so we can change this angle to 30 degrees and now that we know this 30 degrees we won't need this 135 anymore starting from the vertex of this angle let's draw out this blue segment and construct a circle with that as the radius now let's find