Question

State the measure of each missing angles​

Answer 1

Angle
`\( a \)` is 57 degrees.

Angle
`\( b \)` is 131 degrees.

Angle
`\( c \)`is 254 degrees.

The image depicts a set of intersecting lines forming angles. To find the measure of each missing angle labeled as
`\( a \), \( b \), and \( c \)`, we can use the properties of angles formed by intersecting lines.

Here are the properties that can be used:

Vertical angles are equal.

The sum of angles around a point is 360 degrees.

The sum of angles on a straight line is 180 degrees.

Given:

- One angle is given as 49 degrees.

- Another angle is given as 57 degrees.

To find angle
`\( a \)`:

Angle
`\( a \)`is vertical to the 57-degree angle, so
`\( a = 57 \)` degrees.

To find angle
`\( b \)`:

Angle
`\( b \)` and the 49-degree angle are on a straight line, so
`\( b = 180 - 49 \)` degrees.

To find angle
`\( c \)`:

Angle
`\( c \)`, the 57-degree angle, and the angle opposite to the 49-degree angle (which is also 49 degrees because they are vertical angles) are around a point. So,
`\( c = 360 - (57 + 49 + 49) \)` degrees.

Using these properties, can calculate the measures of angles
`\( a \), \( b \), and \( c \)`.

The measures of the missing angles are as follows:

Angle
`\( a \)` is 57 degrees.

Angle
`\( b \)` is 131 degrees.

Angle
`\( c \)`is 254 degrees.