The values of m∠26 = m∠1 + m∠9 = 26° + 44° = 70° and m∠28 = m∠4 + m∠9 = 53° + 44° = 97°.
The measures of the angles of a triangle must add up to 180 degrees. Based on the given information, we can write down the following equations for triangles DEF, DFE, and DEF:
Triangle DEF: m∠D + m∠E + m∠F = 180°
Triangle DFE: m∠D + m∠F + m∠E = 180°
Triangle DEF: m∠E + m∠F + m∠D = 180°
We are given that m∠1 = 26°, m∠4 = 53°, and m∠9 = 44°. We can also see from the diagram that m∠26 = m∠1 + m∠9 and m∠28 = m∠4 + m∠9.
Substituting these values into the equations above, we get:
Triangle DEF: 26° + m∠E + m∠F = 180°
Triangle DFE: 26° + m∠F + m∠E = 180°
Triangle DEF: m∠E + m∠F + 26° = 180°
Adding the first two equations, we get:
2 * (26° + m∠E + m∠F) = 360°
52° + 2 * m∠E + 2 * m∠F = 360°
Subtracting the third equation from this equation, we get:
52° + 2 * m∠E + 2 * m∠F - (m∠E + m∠F + 26°) = 360° - 180°
52° + m∠E + m∠F - 26° = 180°
m∠E + m∠F = 154°
Now we can plug this value back into any of the triangle equations to solve for one of the missing angles. For example, using the first equation:
26° + m∠E + m∠F = 180°
26° + 154° = m∠D
m∠D = 180°
Therefore, m∠26 = m∠1 + m∠9 = 26° + 44° = 70° and m∠28 = m∠4 + m∠9 = 53° + 44° = 97°.
The question probable may be:
In the figure below, which is not drawn to scale, you are given that m∠1 = 26°, m∠4 = 53°, m∠9 = 44°, and m∠13 = 111°. Find the m∠26 and m∠28