Subjects geometry

Angle Values 2028E0

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1. **State the problem:** We have a triangle with angles 70°, 119°, 28°, and two unknown angles labeled $x$ and $y$. We need to find the values of $x$ and $y$, and analyze how changing some angles affects the 119° angle. 2. **Recall the angle sum rule:** The sum of angles on a straight line is 180°, and the sum of angles in a triangle is 180°. 3. **Find $x$:** Since $x$ and 28° are adjacent angles on a straight line, their sum is 180°. $$x + 28 = 180$$ $$x = 180 - 28 = 152$$ 4. **Find $y$:** The angle $y$ is adjacent to 119° on a straight line, so their sum is also 180°. $$y + 119 = 180$$ $$y = 180 - 119 = 61$$ 5. **Analyze the effect of changing angles:** When the 70° angle changes to 86°, and $x$ changes to 36°, we check how the 119° angle changes. Since the angles on a straight line sum to 180°, the angle adjacent to $x$ is: $$180 - x = 180 - 36 = 144$$ The original 119° angle is part of the triangle formed, but with the new angles, the sum of angles around the point must still be 360°. The 119° angle will adjust accordingly, but since the problem does not provide explicit relationships, we conclude the 119° angle will decrease to maintain the total 360° around the point. **Final answers:** $$x = 152$$ $$y = 61$$