Math Problem Statement

Find the missing angles in the given triangle problems.

Solution

These problems involve determining the missing angle in triangles, which can be solved using the triangle angle sum property. The sum of the angles in any triangle is always 180180^\circ.

Let's solve each one:

  1. Problem 1:

    • Given: 3737^\circ and 6464^\circ
    • Sum of angles = 180180^\circ
    • So, s=180(37+64)=180101=79s = 180^\circ - (37^\circ + 64^\circ) = 180^\circ - 101^\circ = 79^\circ

    Answer: s=79s = 79^\circ

  2. Problem 2:

    • Given: 110110^\circ and 162162^\circ
    • The angle aa seems to be external to the triangle. For external angles, the external angle is equal to the sum of the two non-adjacent interior angles.
    • So, a=162110=52a = 162^\circ - 110^\circ = 52^\circ

    Answer: a=52a = 52^\circ

  3. Problem 5:

    • Given: 114114^\circ and 147147^\circ (This also seems to involve an external angle.)
    • h=147114=33h = 147^\circ - 114^\circ = 33^\circ

    Answer: h=33h = 33^\circ

  4. Problem 6:

    • Given: 4141^\circ and 139139^\circ
    • Use the triangle angle sum property:
    • k=180(41+139)=180180=0k = 180^\circ - (41^\circ + 139^\circ) = 180^\circ - 180^\circ = 0^\circ

    Answer: k=0k = 0^\circ

Would you like more details or explanations on any specific part of this solution?

Here are 5 related questions to practice:

  1. If two angles of a triangle are 45° and 90°, what is the third angle?
  2. Can the sum of two angles of a triangle ever exceed 180°?
  3. What is the value of the exterior angle of a triangle if the two opposite interior angles are 50° and 60°?
  4. How do you calculate the third angle in a triangle when the other two angles are known?

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Math Problem Analysis

Mathematical Concepts

Triangle Angle Sum Property
External Angle Theorem

Formulas

Sum of angles in a triangle = 180 degrees
External angle = sum of non-adjacent interior angles

Theorems

Triangle Angle Sum Theorem
External Angle Theorem

Suitable Grade Level

Grades 7-9