∠c and ∠d are vertical angles with m∠c = -3x + 58 and m∠d = x - 2 . What is m∠d?

Solution:

Given, ∠C and ∠D are vertical angles.

The measure of ∠C = -3x + 58

∠D = x - 2.

We have to find the measure of ∠D.

Vertical angles are a pair of opposite angles formed by intersecting lines.

In the figure, ∠A  and  ∠B are vertical angles. So are ∠C  and  ∠D.

Vertical angles are always congruent. So, in this figure,

∠A ≅ ∠B and ∠C ≅ ∠D

So, ∠C = ∠D

-3x + 58 = x - 2

By grouping,

-3x - x = -2 - 58

By further calculation

-4x = - 60

4x = 60

Dividing both sides by 4

x = 60/4

x = 15

So, ∠D = x - 2 = 15 - 2 = 13

Therefore, the value of ∠D is 13.

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∠c and ∠d are vertical angles with m∠c = -3x + 58 and m∠d = x - 2 . What is m∠d?

Summary:

∠C and ∠D are vertical angles with m∠C = -3x + 58 and m∠D = x - 2, then m∠D = 13.