The measure of the angle 1 in degrees is 48°. Since angels 3 and 5 are alternate angles, angle 1 is measured.
What are verticle angles?
The angles that occur at the opposite side of the transverse line are said to be verticle angles. Their sizes are the same. (they are always congruent)
Calculating the measure of angle 1:
From the given figure,
The lines make 5 angles as ∠1, ∠2, ∠3, ∠4, and ∠5.
The angles ∠1, ∠2, and ∠5 form a line with a complete angle of 180°
So, we can write
∠1 + ∠2 + ∠5 = 180°
From the figure, ∠2 = 90°, ∠3 and ∠5 are verticle angles (opposite side of the transverse) and it is given that ∠3 is 42°
Thus, ∠3 = ∠5 = 42°
On substituting all these for finding angle 1,
∠1 + ∠2 + ∠5 = 180°
⇒ ∠1 + 90° + 42° = 180°
⇒ ∠1 = 180° - 132°
⇒ ∠1 = 48°
Therefore, the angle 1 measures 48°.
Learn more about the pair of angles here:
https://brainly.com/question/26167358
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