The OCR of the image is: -- OCR Start -- 14 ВПР. Математика. 7 класс. Вариант 1. Часть 2 Код 7 о оч в точках К CM/F D Параллельные прямые АВ и CD пересекают прямую им соответственно. Угол FMD равен 34°. Найдите угол АКМ. Решение Ответ: B E -- OCR End --

Solution:

Hello! Let's tackle this geometry problem step-by-step.

We are given that parallel lines AB and CD are intersected by a transversal line EF at points K and M, respectively. We know that angle FMD is 34°. We need to find the measure of angle AKM.

Let's use the properties of angles formed by parallel lines and a transversal:

• Vertically opposite angles are equal.
• Adjacent angles on a straight line sum up to 180°.
• Alternate interior angles are equal.
• Corresponding angles are equal.
• Consecutive interior angles sum up to 180°.

Looking at the diagram:

• Angle FMD and angle EMC are vertically opposite angles. Thus, EMC = 34°.
• Angle FMD and angle AKF are corresponding angles. Since AB || CD, corresponding angles are equal. Therefore, AKF = 34°.
• Angle AKM and angle AKF are adjacent angles on a straight line (line AB). Their sum is 180°.
• So, ∠AKM + ∠AKF = 180°.
• Substituting the value of ∠AKF: ∠AKM + 34° = 180°.
• Solving for ∠AKM: ∠AKM = 180° - 34°.
• ∠AKM = 146°.

Alternatively:

• Angle FMD = 34°.
• Angle CMK is vertically opposite to angle FMD. So, CMK = 34°.
• Angle AKM and angle CMK are adjacent angles on a straight line (line EF). No, they are not adjacent on line EF.
• Angle AKM and angle CMK are adjacent angles on the straight line AB. No, they are adjacent angles that form a straight line.
• Angle AKM and angle CMK are supplementary angles because they form a linear pair along the line segment AK. No, this is incorrect. They form a linear pair along the line segment KM.
• Angle AKM and angle CMK are supplementary angles because they form a linear pair along the line AB.
• Correct approach: Angle AKM and angle CMK are adjacent angles on the straight line AB. This is incorrect.
• Let's re-evaluate: Angle FMD = 34°. Angle CMK = 34° (vertically opposite to ∠FMD). Angle AKM and angle CMK are adjacent angles that form the straight angle ∠AKC. No, this is also incorrect.
• The correct relationship is that angle AKM and angle CMK form a linear pair along the straight line AB. No.
• Angle AKM and angle CMK are adjacent angles that form the straight angle ∠AKC. No.
• Let's use the corresponding angles first: Angle FMD = 34°. Angle AKF is the corresponding angle to FMD. Therefore, AKF = 34°. Angle AKM and angle AKF are supplementary angles (they form a linear pair on the straight line AB). Thus, AKM = 180° - AKF = 180° - 34° = 146°.

Final Answer:

The measure of angle AKM is 146°.

Answer: 146°