Find the missing angles in the following triangles.

Let’s solve each triangle one by one.

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Triangle 1 (top left):
Angles given: 45° and 70°. We need to find angle x.
We know that the sum of angles in any triangle is always 180°.
So, x = 180° - 45° - 70°
x = 180° - 115°
x = 65°

✔ Check: 45 + 70 + 65 = 180 → Correct.

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Triangle 2 (top right):
One angle is 110°, and the other two are both labeled “x” — meaning they’re equal.
So, we have: x + x + 110° = 180°
That’s 2x + 110° = 180°
Subtract 110° from both sides: 2x = 70°
Divide by 2: x = 35°

✔ Check: 35 + 35 + 110 = 180 → Correct.

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Triangle 3 (bottom left):
This one has a straight line outside the triangle with an angle labeled “x” and another labeled “y” next to it. Inside the triangle, we have 62° and 51°.

First, let’s find the third angle inside the triangle (the one at the bottom left corner).
Sum of angles in triangle = 180°
So, that missing interior angle = 180° - 62° - 51° = 67°

Now, look at the straight line: angles on a straight line add up to 180°.
The angle labeled “y” is adjacent to the 67° interior angle — so y + 67° = 180°
→ y = 180° - 67° = 113°

Angle “x” is on the same straight line as “y”, so x + y = 180°
But wait — actually, looking again: the diagram shows “x” and “y” forming a straight line together? Or is “x” the exterior angle?

Actually, re-examining: the arrow points left, and “x” is outside the triangle, next to “y”. It looks like “x” and “y” are adjacent angles on a straight line, and “y” is inside the triangle? No — actually, “y” is likely the interior angle at that vertex, and “x” is the exterior angle.

Wait — better approach: In triangle geometry, an exterior angle equals the sum of the two opposite interior angles.

In this triangle, the two known interior angles are 62° and 51°. The exterior angle at the third vertex (which is labeled “x”) should equal 62° + 51° = 113°.

Then, since “x” and “y” are on a straight line, x + y = 180° → y = 180° - 113° = 67°.

Alternatively, if “y” is the interior angle, then y = 180° - 62° - 51° = 67°, and x (exterior) = 180° - 67° = 113°.

Either way, consistent.

So:
- x = 113°
- y = 67°

✔ Check: 62 + 51 + 67 = 180 → Correct. Exterior angle x = 62 + 51 = 113 → Correct.

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Triangle 4 (bottom right):
We see an exterior angle of 120°, and one interior angle is 70°. We need to find x and y.

First, note: the 120° angle is adjacent to angle x — they form a straight line. So:

x + 120° = 180° → x = 60°

Now, in the triangle, we have angles: 70°, x (which is 60°), and y.

Sum = 180° → 70 + 60 + y = 180 → 130 + y = 180 → y = 50°

✔ Check: 70 + 60 + 50 = 180 → Correct.

Also, exterior angle theorem: exterior angle (120°) should equal sum of two opposite interior angles: 70° + y → 70 + 50 = 120 → Correct.

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Final Answers:

Top left: x = 65°
Top right: x = 35°
Bottom left: x = 113°, y = 67°
Bottom right: x = 60°, y = 50°

Final Answer:
Top left: x = 65°
Top right: x = 35°
Bottom left: x = 113°, y = 67°
Bottom right: x = 60°, y = 50°