Question

Can someone pls help me?

Determine the measures of the unknown angles in the
figure below.

Answer 1

x= 127

w = 53

Explanation:

Answer 2

In triangles ABC and ADE, the unknown angles are determined step by step. Angle w is 53°, angle y is 39°, and angle x is 95°. These values are obtained using the Triangle Sum Theorem and Angle Sum Property.

To determine the measures of the unknown angles in triangles ABC and ADE, we can follow these steps:

1. Use the Triangle Sum Theorem in Triangle ABC:

`\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180^\circ \]`

`\[ w + 42^\circ + 85^\circ = 180^\circ \]`

`\[ w = 53^\circ \]`

2. Use the Triangle Sum Theorem in Triangle ADE:

`\[ \text{Angle D} + \text{Angle E} + \text{Angle A} = 180^\circ \]`

`\[ y + 88^\circ + 53^\circ = 180^\circ \]`

`\[ y = 39^\circ \]`

3. Use the Angle Sum Property in Triangle ABC:

`\[ \text{Angle BAC} + \text{Angle ABC} + \text{Angle BAE} = 180^\circ \]`

`\[ w + 42^\circ + x = 180^\circ \]`

`\[ x = 95^\circ \]`

In summary:

-
`\( w = 53^\circ \)`

-
`\( y = 39^\circ \)`

-
`\( x = 95^\circ \)`

These are the measures of the unknown angles in triangles ABC and ADE.