Question

find the measure of the numbered angles in each rectangle​

Answer 1

Given:-

• A rectangle with one diagonal

To Find:-

• The measure of all the numbered angles.

Note:-

• Before solving we need to label the figure. Refer to the attachment.

Solution:-

From the figure we can see,

∠DAC = 58°

∠CAB = ∠4

We know,

Each angle of a rectangle is right - angled (90°)

Hence,

∠CAB + ∠DAC = 90°

=> ∠4 + 58° = 90°

=> ∠4 = 90° - 58°

=> ∠4 = 32°

Hence,

∠CAB = ∠4 = 32°

Now,

∠CAB = ∠ACD = 32° [Alternative Angles]

Hence,

∠1 = 32°

Now,

∠ACD + ∠ACB = 90°

= 32° + ∠2 = 90°

=> ∠2 = 90° - 32°

=> ∠2 = 58°

Now,

In ∆ABC

∠CAB = 32°

∠ACB = 58°

According to angle-sum property of a triangle,

∠ACB + ∠CAB + ∠ABC = 180°

=> 58° + 32° + ∠3 = 180°

=> 90° + ∠3 = 180°

=> ∠3 = 180° - 90°

=> ∠3 = 90°

Now,

In ∆ADC,

∠CAD = 58°

∠ACD = 32°

According to angle-sum property of the triangle,

∠CAD + ∠ACD + ∠CDA = 180°

=> 58° + 32° + ∠5 = 180°

=> 90° + ∠5 = 180°

=> ∠5 = 180° - 90°

=> ∠5 = 90°

Hence,

• ∠1 = 32°
• ∠2 = 58°
• ∠3 = 90°
• ∠4 = 32°
• ∠5 = 90°

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