Angles 1, 2, and 3 measure 56°, 90°, and 56°, in that order.
In the given scenario, you have an angle x equal to 34°.
To determine the measures of adjacent angles, you use the information that adjacent angles share a common vertex and a common side but do not overlap.
Let ∠1 be an angle adjacent to x.
According to the figure, the sum of angles in a straight line is 180°. So, you have:
90°+34°+∠1=180°
90°+34°+∠1=180°
Solving for ∠1:
124°+∠1=180°
124°+∠1=180°
∠1=180°−124°
∠1=180°−124°
∠1=56°
∠1=56°
Since ∠1 is adjacent to x, ∠1 is also equal to ∠3 due to vertically opposite angles. Additionally, ∠2 is a right angle, given as 90°.
Therefore, the measures of angles 1, 2, and 3 are 56°, 90°, and 56°, respectively.
This result aligns with the properties of adjacent angles and the angles formed in a straight line, providing a clear understanding of the relationships between these angles in the given geometric configuration.
Question
If x=34° find the measures of angles 1,2,3 .