Question

Monitoring Progress and Modeling with Mathematics In Exercises 3-6, find the Indicated measure. Explain your reasoning. (See Example 1.) 4. OR 10. 3. GH 46 H M M 36 36 G In Exereises 11-14, find the indicated measure. Explain your reasoning. (See Example 3) 11. M ABD 12. PS 5. AB 6. UW W 7x + 13 5x Bar 13. MZRUL 14. FG In Exercises 7-10, tell whether the information in the diagram allows you to conclude that point Plies on the perpendicular bisector CEM. Explain your reasoning, (See Example 2) 小 V FTX + 11 7. x 1 a H Our 10 M M M 306 Chapter 6 Relationships within Triangles P M Р M 306 Chapter 6 Relationships Within Triangles In Exercises 15 and 16, tell whether the information in the diagram allows you to conclude that EX bisects ZFEG. Explain your reasoning. (See Example 4.) 15. 16. In Exercises 17 and 18, tell whether the information in the diagram allows you to conclude that DB = DC. Explain your reasoning. 17. 18. A

Answer 1

The measure of angle GHM is 74 degrees.

Step-by-step explanation:

In triangle GHM, we can use the Triangle Angle Sum Theorem, which states that the sum of the interior angles of a triangle is always 180 degrees. Given that angle H is 46 degrees and angle M is 36 degrees, we can find angle GHM by subtracting the sum of angles H and M from 180 degrees:

`\[ \angle GHM = 180 - (\angle H + \angle M) \]`

`\[ \angle GHM = 180 - (46 + 36) \]`

`\[ \angle GHM = 180 - 82 \]`

`\[ \angle GHM = 98 \]`

So, angle GHM measures 98 degrees.

In this explanation, we applied the Triangle Angle Sum Theorem to find the measure of angle GHM in triangle GHM. The theorem provides a fundamental relationship between the interior angles of a triangle and allows us to express the measure of one angle in terms of the measures of the other two angles. By substituting the given values for angles H and M into the formula, we derived the measure of angle GHM.

This process is crucial in geometry as it enables us to deduce angle measures based on known information about a geometric figure. The step-by-step calculation demonstrates the application of mathematical principles in solving geometric problems.