The angle between the two altitudes of a parallelogram through the same vertex of an obtuse angle of the parallelogram is 30°. The measure of the obtuse angle is
(a) 100°
(b) 150°
(c) 105°
(d) 120°

Solution:

Given, the angle between the two altitudes of a parallelogram through the same vertex of an obtuse angle of the parallelogram is 30°.

We have to find the measure of the obtuse angle.

Consider a parallelogram ABCD

Let EC and FC be the altitudes

Given, ∠ECF = 30°

Let ∠EDC = x

We know that the opposite angles in a parallelogram are equal.

So, ∠FBC = x

By angle sum property of a triangle,

∠DCE = 180° - (90° + x) = 90° - x

Similarly, ∠BCF = 90° - x

We know that the sum of adjacent angles of a parallelogram are supplementary.

So, ∠ADC + ∠DCB = 180°

∠ADC + (∠DCE + ∠ECF + ∠BCF) = 180°

x + 90° - x + 30° + 90° - x = 180°

x - 2x + 210° = 180°

x = 210° - 180°

x = 30°

Now, ∠DCB = 90° - 30° + 30° + 90° - 30°

= 180° - 30°

= 150°

Therefore, the required obtuse angle is 150°

✦ Try This: The sum of all interior angles of a parallelogram is (a) 180°, (b) 120°, (c) 360°, (d) 90°

☛ Also Check: NCERT Solutions for Class 8 Maths

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NCERT Exemplar Class 8 Maths Chapter 5 Problem 34

The angle between the two altitudes of a parallelogram through the same vertex of an obtuse angle of the parallelogram is 30°. The measure of the obtuse angle is (a) 100° (b) 150° (c) 105° (d) 120°

Summary:

The angle between the two altitudes of a parallelogram through the same vertex of an obtuse angle of the parallelogram is 30°. The measure of the obtuse angle is 150°.

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