DAV Class 7 Maths Chapter 8 Worksheet 1
Triangle And Its Properties Worksheet 1
1. Look at the figure carefully and complete the statements.
(a) \(\angle \text{BAY} = \angle \text{ABC } + \) _____
Answer \( \angle \text{BAY} = \angle \text{ABC } + \) \( {\boxed{ \color{red} \angle \text{ACB}}}\)
(b) \(\angle \text{CBZ} = \) _____ \( + \) _____
Answer \( \angle \text{CBZ} = \) \({\boxed{ \color{red} \angle \text{CAB } + \angle \text{BCA}}}\)
(c) ______ \(= \angle \text{CAB} + \angle \text{ABC} \)
Answer \({\boxed{\color{red} \angle \text{ACX }}}\) \(= \angle \text{CAB} + \angle \text{ABC} \)
2. In the given figure, find-
(a) \( \angle \text{YRQ}\)
Solution
\begin{align*} \angle \text{YRQ} & = \angle \text{P} + \angle \text{Q} \\ \angle \text{YRQ} & = 60^\circ + 70^\circ \\ \angle \text{YRQ} & = 130^\circ \\ \end{align*}
Answer \( \angle \text{YRQ} = \color{red} 130^\circ\)
(b) \( \angle \text{PRQ}\)
Solution
\begin{align*} \text{Angle sum property:} \\ \angle \text{P} + \angle \text{R} + \angle \text{Q} &= 180^\circ \\ 60^\circ + \angle \text{R} + 70^\circ &= 180^\circ \\ 130^\circ + \angle \text{R} &= 180^\circ \\ \angle \text{R} &= 180^\circ - 130^\circ \\ \angle \text{R} &= 50^\circ \\ \end{align*}
Answer \( \angle \text{PRQ} = \color{red} 50^\circ\)
3. One of the exterior angle of a \( \color{black} \triangle ABC \) measures \( \color{black} 150^\circ \). If one of the interior opposite angle is \( \color{black} 75^\circ \). Find the other interior opposite angle. What type of triangle is this?
Solution
In a triangle, the exterior angle is equal to the sum of the two interior opposite angles \begin{align*} \angle \text{A} + \angle \text{C} & = \angle \text{DBC}\\ 75^\circ + \angle \text{C} & = 150^\circ \\ \angle \text{C} & = 150^\circ - 75^\circ \\ \angle \text{C} &= 75^\circ \\ \\ \angle \text{C} = 75^\circ ,& \angle \text{A} = 75^\circ \\ \text{BC} &= \text{BA} \end{align*}
Answer The other interior opposite angle is \({\boxed{ \color{red} 75^\circ}}\) and its an \({\boxed{ \color{red} \text{Isosceles triangle}}}\).
4. One of the exterior angles of triangle is \( \color{black} 100^\circ \). The interior opposite angles are equal to each other. Find the measure of these equal interior opposite angles.
Solution
In a triangle, the exterior angle is equal to the sum of the two interior opposite angles. \begin{align*} \angle \text{A} + \angle \text{C} &= \angle \text{DBC}\\ \angle \text{A} &= \angle \text{C} \color{green} \text{ (Given)} \\ \angle \text{A} + \angle \text{A} &= 100^\circ \\ 2 \angle \text{A} &= 100^\circ \\ \angle \text{A} &= \frac{100^\circ}{2} \\ \angle \text{A} &= 50^\circ \\ \angle \text{C} &= 50^\circ \\ \end{align*}
Answer The measures of equal interior opposite angles are \({\boxed{ \color{red} 50^\circ , 50^\circ}}\)
5. In a triangle one of the exterior angle is \( \color{black} 105^\circ \). One of the interior opposite angle is \( \color{black} 75^\circ \). Find the measure of all the angles of the triangle.
Solution
In a triangle, the exterior angle is equal to the sum of the two interior opposite angles. \begin{align*} \angle \text{A} + \angle \text{C} &= \angle \text{DBC}\\ 75^\circ + \angle \text{C} &= 105^\circ \\ \angle \text{C} &= 105^\circ - 75^\circ \\ \angle \text{C} &= 30^\circ \\ \\ \angle \text{DBC} + \angle \text{ABC} &= 180^\circ \text{ (Linear Pair)} \\ 105^\circ + \angle \text{ABC} &= 180^\circ \\ \angle \text{ABC} &= 180^\circ - 105^\circ \\ \angle \text{ABC} &= 75^\circ \\ \end{align*}
Answer The measures of remaining angles is \({\boxed{ \color{red} 30^\circ , 75^\circ}}\)
6. In the given triangle, find the measure of \( \color{black} \angle \text{PRQ} \)
Solution
In a triangle, the exterior angle is equal to the sum of the two interior opposite angles. \begin{align*} \angle \text{R} + \angle \text{P} &= \angle \text{RQS}\\ \angle \text{R} + 90^\circ &= 140^\circ \\ \angle \text{R} &= 140^\circ - 90^\circ \\ \angle \text{R} &= 50^\circ \\ \\ \end{align*}
Answer The measure of \( \angle \text{PRQ} = {\boxed{ \color{red} 50^\circ}}\)