Given <1 congruent<5 Prove: <1 is supplementary to <4
1 answer:
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In all right triangles, the ratio between a leg and the hypothenuse is the sine of the angle opposite to the leg.
So, in your case, we have
In order to find XY, we have
So, the ratio for the sine is
Answer:
∠1 = 93°
∠2 = 35°
∠3 = 52°
∠4 = 35°
∠5 = 93°
∠6 = 128°
∠7 = 52°
∠8 = 128°
∠9 = 52°
∠10 = 93°
∠11 = 87°
∠12 = 93°
Step-by-step explanation:
Here are some things you need to remember:
Supplementary angles are angles that sum up to 180° or they form a straight line.
Corresponding angles are congruent. Corresponding angles are angles that are in the same corner or the same side of the intersection.
Alternating angles are congruent. Alternating angles are angles found on alternate sides of the intersecting line. You have interior alternating angles, so these are alternating angles inside the parallel lines, and you have exterior alternating angles, angles found alternating outside the parallel lines.
Vertical angles are opposite angles made by two lines that intersect. Vertical angles are congruent or they have the same measure.
Attached are examples of each, so you can visualize it yourself.
Let's solve these angles with that in mind (let's show the easier ones first):
<u>∠11 is vertical to the angle that measures 87°</u>
This means that they are congruent. And so we know that
∠11 = 87°
<u>∠10 is supplementary to angle that measures 87°</u>
This means that if we add them up together, we will get 180°.
∠10 + 87° = 180°
Subtract 87° from both sides of the equation:
∠10 + 87° - 87° = 180° - 87°
∠10 = 93°
<u>∠12 is vertical to ∠10</u>
This means that ∠12 = ∠10
∠10 = 93°
∠12 = ∠10
∠12 = 93°
<u>∠1 and ∠10 are corresponding angles. </u>
So this means that they are congruent.
∠1 = ∠10
∠10 = 93°
∠1 = ∠93°
<u>∠1 is vertical to ∠5</u>
This means that they are congruent:
∠1 = ∠5
∠1 = 93°
∠5 = 93°
<u>∠3 is vertical to the angle that measures 52°</u>
This means that they are congruent:
∠3 = 52°
<u>∠3 and ∠7 are corresponding angles.</u>
This means that they are congruent.
∠3 = ∠7
∠3 = 52° by substitution we can say then:
52° = ∠7
<u>∠7 and ∠9 are vertical angles.</u>
This means that they are congruent:
∠7 = ∠9
∠7 = 52°
52° = ∠9
<u>∠9 and ∠6 are supplementary. This means that their sum add up to 180°.</u>
∠6 + ∠9 = 180°
∠9 = 52°
∠6 + 52° = 180°
Subtract both sides by 52°
∠6 + 52° - 52° = 180° - 52°
∠6 = 128°
<u>∠6 and ∠8 are vertical angles:</u>
This meas that they are congruent.
∠6 = ∠8
∠6 = 128°
128° = ∠8
<u>∠3 combined with ∠4 is alternate (interior) to the angle that measures 87°</u>
This means that if we add up ∠3 and ∠4 it will be equal to 87°
∠3 + 4 = 87°
∠3 = 52°
52° + ∠4 = 87°
Subtract 52° from both sides:
52° - 52° + ∠4 = 87° - 52°
∠4 = 35°
<u>∠4 and ∠2 are vertical angles:</u>
This means that they are congruent.
∠4 = ∠2
∠4 = 35°
35° = ∠2
