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erastova [34]
3 years ago
11

"What is the sum of the measures of the interior angles formed by the boundary of this team pennant?

Mathematics
1 answer:
professor190 [17]3 years ago
3 0
If the team pennant is triangular then the correct answer is C) 180 degrees

That is because the sum of all angles in a triangle is always 180. An easy example is a right triangle in which the right angle is 90, and the remaining two are 45.
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1. SSS

2. SAS

3. SAS

4. SSS

5. SAS

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1) Side FY ≅ Side CW  Given

Side FP ≅ Side CM     Given

Side YP ≅ Side MW    Given

∴ΔMCW ≅ ΔFPY by the Side-Side-Side (SSS) rule of congruency

2) ∠CBD ≅ ∠BCA given that both are alternate interior angles

Side EB ≅ Side EC and Side DB ≅ Side CA Given

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3. ∠SVU ≅ ∠SVT   Given

Side SV ≅ Side SV  by reflexive property

Side VT ≅ Side VU   Given

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4. Side MN ≅ Side QP  Given

Side MQ ≅ Side NP     Given

Side NQ ≅ Side NQ    by reflexive property

∴ΔQNM ≅ ΔQNP by the Side-Side-Side (SSS) rule of congruency

5. Indirect proof

Side GL ≅ Side HL  Given

Side GJ ≅ Side HK     Given

∠JLG ≅ ∠HLK    vertically opposite angles

By sine rule

GJ/sin(∠JLG) = GL/n(∠GJL)

Similarly

HK/sin(∠HLK) = HL/n(∠HKL)

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6. ∠XZY ≅ ∠XZW   Supplementary ∠s with ∠XZY = 90°

Side XZ ≅ Side XZ  by reflexive property

Side ZW ≅ Side ZY   Given

∴ ΔXYZ ≅ ΔXWZ by Side-Angle-Side (SAS) rule of congruency.

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