Given the following diagram, find the missing measure. G

Mathematics

1 answer:

jonny [76]3 years ago

6 0

The Given Triangle PMO is a Right Angled Triangle with m∠M = 90°

Given m∠P = 40°

We know that : Sum of Angles in a Triangle = 180°

⇒ m∠P + m∠M + m∠O = 180°

⇒ 40° + 90° + m∠O = 180°

⇒ 130° + m∠O = 180°

⇒ m∠O = 180° - 130°

⇒ m∠O = 50°

We can notice that m∠O and m∠1 form a Linear Pair (180°)

⇒ m∠O + m∠1 = 180°

⇒ 50° + m∠1 = 180°

⇒ m∠1 = 180° - 50°

⇒ m∠1 = 130°

Last Option is the Answer

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<h3>Answer: (4,2)</h3>

==============================================================

Explanation:

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Reflecting over y = 1 lands the point on (0,2) because we move 1 unit up to arrive at the line of reflection, and then we keep going one more unit (same direction) to complete the full reflection transformation. I'll call this point P.

Then we reflect point P over the line x = 2 to arrive at the location Q = (4,2). Note how we moved 2 units to the right to get to the line of reflection, and then keep moving the same direction 2 more units, then we have applied the operation of "reflect over the line x = 2"

So we have started at C = (0,0), moved to P = (0,2) and then finally arrived at the destination Q = (4,2). This is the location of C' as well.

All of this is shown in the diagram below.