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Lines and Angles — MATHS STD 7 — Question

Gujarat BoardEnglish MediumSTD 7MATHSLines and Angles1 Mark
MCQ
In Fig. if $AOB$ and $COD$ are straight lines, then:
  • A
    $x = 29, y = 100$
  • B
    $x = 110, y = 29$
  • ✓
    $x = 29, y = 110$
  • D
    $x = 39, y = 110$
✓

Answer

Correct option: C.
$x = 29, y = 110$
$\angle \text{AOD}+\angle \text{BOD}=180^\circ$ [Linear pair angles]
$\Rightarrow \text{y}^\circ+70^\circ=180^\circ$
$\Rightarrow \text{y}^\circ=110^\circ$
$\Rightarrow \text{y}=110$
Now, $\angle \text{AOC}= \angle \text{BOD}=70^\circ$ [Vertically opposite angles]
Now, $\angle \text{AOC}+\angle \text{COE}+\angle \text{EOB}+\angle \text{BOD}+\angle \text{AOD}=360^\circ$ [Complete angle]
$\Rightarrow 70^\circ+28^\circ+(3\text{x}-5)^\circ+70^\circ+110^\circ=360^\circ$
$\Rightarrow (3\text{x})^\circ+273^\circ=360^\circ$
$\Rightarrow3\text{x}=87$
$\Rightarrow \text{x}=29$
Hence, the correct answer is option $(c).$

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