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ML Aggarwal Solutions Class 9 Mathematics Solutions for Rectilinear Figures Exercise 13.1 in Chapter 13 - Rectilinear Figures
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(a) In figure (1) given below, ABCD is a parallelogram in which ∠DAB = 70°, ∠DBC = 80°.
Calculate angles CDB and ADB.
(b) In figure (2) given below, ABCD is a parallelogram. Find the angles of the AAOD.
(c) In figure (3) given below, ABCD is a rhombus. Find the value of x.
(a) Since, ABCD is a || gm
We have, AB || CD
\begin{aligned} &\angle \mathrm{ADB}=\angle \mathrm{DBC} \quad \text { (Altemate angles) }\\ &\angle \mathrm{ADB}=80^{\circ} \quad\left(\text { Given, } \angle \mathrm{DBC}=80^{\circ}\right) \end{aligned}
Now,
\begin{aligned} &\text { In } \triangle \mathrm{ADB}, \text { we have }\\ &\angle \mathrm{A}+\angle \mathrm{ADB}+\angle \mathrm{ABD}=180^{\circ} \quad \text { (Angle sum property of a triangle) }\\ &70^{\circ}+80^{\circ}+\angle \mathrm{ABD}=180^{\circ}\\ &150^{\circ}+\angle \mathrm{ABD}=180^{\circ}\\ &\angle \mathrm{ABD}=180^{\circ}-150^{\circ}=30^{\circ} \end{aligned}
Now, ∠CDB = ∠ABD (Since, AB || CD and alternate angles)
So,
\begin{array}{l} \angle \mathrm{CDB}=30^{\circ} \\ \text { Hence, } \angle \mathrm{ADB}=80^{\circ} \text { and } \angle \mathrm{CDB}=30^{\circ} \text { . } \end{array}
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