Maharashtra BoardEnglish MediumSTD 7MathsProperties of Triangles4 Marks
Question
Find x, y, z (whichever is required) from the figure given below:
✓
Answer
We can see that in $\triangle \text{ADC}, \angle \text{ADC}$ is equal to 90°
$(\triangle \text{ADC}$ is a right triangle$)$
We also know that the sum of all the angles of a triangle is equal to 180°
Which means: 45° + 90° + y = 180° $($Sum of the angles of $\triangle \text{ADC})$
135° + y = 180°
y = 180° - 135°
y = 45°
We can also say that in $\triangle \text{ABC},\angle \text{ABC}+\angle \text{ACB}+\angle \text{BAC}$ is equal to 180°
$($Sum of the angles of $\triangle \text{ABC})$
40° + y + (x + 45°) = 180°
40° + 45° + x + 45° = 180° (y = 45°)
x = 180° - 130°
x = 50°
Therefore, we can say that the required angles are 45° and 50°
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