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olganol [36]
10 months ago
14

I need help with this math problem please. I need help finding proofs and reasons please

Mathematics
1 answer:
shutvik [7]10 months ago
8 0

In order to prove that the angles RST and TUR are congruent, the lines 1, 2 and 3 of statements and reasons are correct.

Since triangles RST and TUR have all three sides congruent, so they are congruent triangles by case SSS.

For the line 4, the statement is "angle RST congruent to angle TUR" (what we want to prove), and the reason is "corresponding angles of congruent triangles".

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∠ACE is formed by two secants intersecting outside of a circle. If minor arc BD = 25°, minor arc AB = 115°, and minor arc DE = 1
dmitriy555 [2]

Answer:

m∠ACE = 40°

Step-by-step explanation:

Consider the below figure attached with this question.

Given information: arc BD = 25°, minor arc AB = 115°, and minor arc DE = 115°.

We need to find the measure of ∠ACE.

minor arc AB + minor arc BD + minor arc DE + minor arc AE = 360°

115° + 25° + 115° + minor arc AE = 360°

255° + minor arc AE = 360°

minor arc AE = 360° - 255°

minor arc AE = 105°

The measure of minor arc AE is 105°.

Using Intersecting secants outside the circle theorem

Angle between two secants = \frac{1}{2}(Major arc - Minor arc)

\angle ACE=\frac{1}{2}[Arc(AE)-Arc(BD)]

\angle ACE=\frac{1}{2}[105-25]

\angle ACE=\frac{1}{2}[80]

\angle ACE=40

Therefore, the measure of ∠ACE is 40°.

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2 years ago
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