Math Problem Statement

What are the measures of the various angles in the four geometry problems?

Solution

Let's analyze and solve the four questions from the uploaded image:

1. What is the measure of angle 1?

  • Given: There is a straight line, and angles are provided as 145° and 40°.
  • Solution: The sum of angles on a straight line is 180°. Let angle 1 be represented by xx. Then: 145+40+x=180145^\circ + 40^\circ + x = 180^\circ Solving for xx: 185+x=180    x=180185=75185^\circ + x = 180^\circ \implies x = 180^\circ - 185^\circ = 75^\circ
  • Answer: 75 degrees (Option C).

2. X=52X = 52^\circ, Z=98Z = 98^\circ. What is the measure of YY?

  • Given: X=52X = 52^\circ, Z=98Z = 98^\circ.
  • Solution: This is a straight line with supplementary angles. The sum of XX, YY, and ZZ should be 180°. 52+Y+98=18052^\circ + Y + 98^\circ = 180^\circ Solving for YY: 150+Y=180    Y=180150=30150^\circ + Y = 180^\circ \implies Y = 180^\circ - 150^\circ = 30^\circ
  • Answer: 30 degrees (Not listed directly, but this might be the closest option).

3. What is the measure of 1\angle 1?

  • Given: There are correspondingdegrees.

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Math Problem Analysis

Mathematical Concepts

Geometry
Angles
Straight Lines
Supplementary Angles

Formulas

Sum of angles on a straight line = 180°
Supplementary angles sum = 180°

Theorems

Angle Sum Property of Straight Lines
Supplementary Angles Theorem

Suitable Grade Level

Grades 6-8