Find Missing Angles (Simple Figures) Worksheets [PDF] (7.G.B.5 ... - Free Printable

Let's solve each problem step by step.

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Problem 1:

Given:
- $\overrightarrow{YZ}$ is a straight line.
- Angle $ \angle XOY = 130^\circ $
- We are to find $ \angle XOZ = x^\circ $

Diagram Interpretation:
Point $O$ lies on the straight line $YZ$. Ray $OX$ comes out from point $O$, forming two angles:
- One angle between $XO$ and $YO$ is $130^\circ$
- The other angle between $XO$ and $ZO$ is $x^\circ$

Since $YZ$ is a straight line, the total angle around point $O$ along the line is $180^\circ$. So:

$$
\angle XOY + \angle XOZ = 180^\circ
$$

Substitute known values:

$$
130^\circ + x^\circ = 180^\circ
$$

Solve for $x$:

$$
x = 180^\circ - 130^\circ = 50^\circ
$$

✔ Answer for Problem 1: $ \boxed{50^\circ} $

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Problem 2:

Given:
- Point $O$ with rays $OG$, $OF$, and $OE$
- $ \angle FOE = 63^\circ $
- $ \angle GOE = x^\circ $ (we need to find $ \angle FOG $)
- There’s a right angle symbol at $ \angle GOE $? Wait — let's look carefully.

Actually, in the diagram:
- $ \angle GOE $ is marked as $x^\circ$
- $ \angle FOE = 63^\circ $
- But there is a right angle symbol at $ \angle GOE $? No — wait: the right angle symbol is at $ \angle GOE $? Let's check again.

Wait — actually, looking at the diagram:

There is a square corner symbol at $ \angle GOE $? Or at $ \angle GOE $? No — the square symbol is at the vertex $O$, between $OG$ and $OE$, meaning that $ \angle GOE = 90^\circ $. That’s the key!

So:
- $ \angle GOE = 90^\circ $
- $ \angle FOE = 63^\circ $
- We are to find $ \angle FOG = x^\circ $

Now, notice that $ \angle GOE $ is made up of $ \angle GOF $ and $ \angle FOE $, so:

$$
\angle GOE = \angle GOF + \angle FOE
$$

$$
90^\circ = x^\circ + 63^\circ
$$

Solve for $x$:

$$
x = 90^\circ - 63^\circ = 27^\circ
$$

✔ Answer for Problem 2: $ \boxed{27^\circ} $

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✔ Final Answers:

1. $ \angle XOZ = \boxed{50^\circ} $
2. $ \angle FOG = \boxed{27^\circ} $

Let me know if you'd like a visual explanation or further clarification!