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Ira Lisetskai [31]
3 years ago
6

Alternate exterior angles ​

Mathematics
1 answer:
exis [7]3 years ago
8 0

Answer:

When  \: two  \: lines  \: are \:  crossed \:  by  \: another \:  line \:  (called  \: the \:  Transversal \: ):  \: Alternate \:  Interior  \: Angles \:  are  \: a \:  pair  \: of  \: angles  \: on \:  the \:  inner  \: side  \: of  \: each  \: of \:  those  \\  \\  \\  \\  \\ two \:  lines  \: but  \: on \:  opposite  \: sides  \: of  \: the  \: transversal.

hope it helps if it helps don'tforget to like and mark

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Can you help? Having a hard time figuring this out. Thanks
Dmitrij [34]

Answer:

3a) The value of  x = 56

3b) The measure of ∠ H T M = 90°

3c) The radius of the circle = 53

Step-by-step explanation:

3a) ∵ A F is a tangent to the circle O at point F

∵ Secant AH intersects circle O at point T

∴ (A F)² = (A T)(A H)

∴ 7( x + 7) = (21)² ⇒ ÷ 7

∴ x + 7 = 63

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3b) ∵ HM is a diameter

∴ The measure of the arc HM = 180° ⇒ semi-circle

∵ ∠ H T M is inscribed angle subtended by the arc HM

∴ m ∠ H T M = half the measure of arc HM

∴ m ∠ H T M = 180° ÷ 2 = 90°

3c) ∵ Δ H T M is a right angle triangle at T

∴ (H M)² = (M T)² + (H T)² ⇒ Pythagorean theorem

∴ (H M)² = (90)² + (56)²

∴ (H M)² = 11236

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Step-by-step explanation:

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3 years ago
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