If you know two angle measures of a triangle in spherical geometry, can you always find the measure of the third angle? Explain.

A. Yes; the angle measures of a triangle always sum to 180.
B. Yes; the angle measures of a triangle always sum to 270 in spherical
geometry.
C. No; the sum of angle measures in spherical geometry is always greater than
180, but there is not a particular number they must sum to.
D. No; the sum of angle measures in spherical geometry is always greater than
270, but there is not a particular number they must sum to.

Question

21-10-2021
Mathematics

contestada

If you know two angle measures of a triangle in spherical geometry, can you always find the measure of the third angle? Explain.

A. Yes; the angle measures of a triangle always sum to 180.
B. Yes; the angle measures of a triangle always sum to 270 in spherical
geometry.
C. No; the sum of angle measures in spherical geometry is always greater than
180, but there is not a particular number they must sum to.
D. No; the sum of angle measures in spherical geometry is always greater than
270, but there is not a particular number they must sum to.

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Help with question 1 please thank you!!!

adioabiola adioabiola · Answer 1 · 2021-10-22T12:48:02+02:00

When two angle measure of a triangle are given in spherical geometry: The sum of angle measures in spherical geometry is always greater than 180, but there is not a particular number they must sum to. Choice C (No) is correct

According to the question;

Two angle measures of a triangle in spherical geometry are given.

However, unlike in plane geometry where affirmatively, the sum of angles in a triangle is equal to 180°.

In spherical geometry;

The totality of the angles of a triangle on a sphere is given as 180°(1 + 4x), where x is the fraction of the sphere's surface that is enclosed by the triangle. For any positive value of x, which in each case exceeds 180°.