Exterior Angle Property

Q.

Consider the figure:

If BC = AC, x = 2y, and angle ACB = 60^o, then find the value of $\angle$A + $\angle$B + $\angle$x + $\angle$y (in degrees).

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Q.

Consider the figure:

If $\angle$A = ${50}^{\circ }$​, $\angle$B = ${70}^{\circ }$​, and x = 2y, then, the value of x (in degrees) is___.

Q.

Consider the figure:

If $\angle$A = ${50}^{\circ }$​, $\angle$B = ${70}^{\circ }$​, and x = 2y, then find the value of y (in degrees).

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Q.

Consider the figure:

Find the value of x + y + $\angle$ACB.

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Q. In the given figure, the value of 'x' and 'y' is:

1. $x={45}^{\circ },y={65}^{\circ }$
2. $x={125}^{\circ },y={65}^{\circ }$
3. $x={125}^{\circ },y={35}^{\circ }$
4. $x={75}^{\circ },y={45}^{\circ }$

Q.

Consider the figure:

If BC = AC, x = 2y, and angle ∠ACB = 60^o, then find the value of ∠B + y (in degrees).

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Q.

In the given figure, $\angle x=$

1. $\angle a+\angle c$

2. $\angle a+\angle b$

3. $\angle b+\angle c$

4. $\angle a+\angle b+\angle c$

Q.

Consider the figure:

If $\angle$B = ${50}^{\circ }$, $\angle$ACD = ${120}^{\circ }$, then find the value of $\angle$A (in degrees).

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Q.

In the given figure, if the bisectors of exterior angle $\angle BCE$ and $\angle CBD$ at I, then $\angle BIC=$___

1. ${90}^{\circ }+\frac{\angle A}{2}$

2. $-{90}^{\circ }-\frac{\angle A}{2}$

3. ${90}^{\circ }-\frac{\angle A}{2}$

4. $-{90}^{\circ }+\frac{\angle A}{2}$

Q.

In the figure, sides $QP$ and $RQ$ of $△PQR$ are produced to points S and T, respectively. If $\angle SPR={135}^{\circ }$ and $\angle PQT={110}^{\circ }$, find $2\angle PRQ.$

1. 

2. 

3. 

4.