Math Problem Statement

Determine the values of the unknown angles in the given diagrams.

Solution

The image you've uploaded contains a set of geometry problems involving angle properties. Let's go through each part to determine the unknown angles:

a) Triangle with angles aa, bb, and cc:

  • You know that one angle is 3030^\circ.
  • In any triangle, the sum of the internal angles is 180180^\circ. Therefore, if one angle is 3030^\circ, and if aa and cc are the other two angles, we can solve for the unknowns: a+b+c=180a + b + c = 180^\circ 30+b+c=18030^\circ + b + c = 180^\circ

b) Adjacent Angles with the angle 7070^\circ and 4343^\circ:

  • Since the angles on a straight line sum to 180180^\circ, we can subtract the known angles from 180180^\circ to find the unknown angle: 180(70+43)180^\circ - (70^\circ + 43^\circ)

c) Triangle with 7070^\circ and 5050^\circ angles:

  • Again, using the fact that the sum of the angles in any triangle is 180180^\circ, we can determine the unknown angle: 70+50+x=18070^\circ + 50^\circ + x = 180^\circ

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Math Problem Analysis

Mathematical Concepts

Triangle Angle Sum
Linear Pair of Angles
Parallel Lines and Transversals

Formulas

Sum of interior angles in a triangle: a + b + c = 180°
Supplementary angles: a + b = 180°

Theorems

Triangle Sum Theorem
Linear Pair Theorem
Alternate Interior Angles Theorem

Suitable Grade Level

Grades 7-9