Question

Find the measure of the indicated angle in each triangle.​

Answer 1

Given:

To find the measure of the indicated angle in each triangle.​

Solution:

Take triangle TUV,

$\[\begin{array}{l}\angle T + \angle U + \angle V = 180^\circ \\ \Rightarrow 37^\circ + \angle U + 63^\circ = 180^\circ \\ \Rightarrow \angle U = 180^\circ - 100^\circ \\ \Rightarrow \angle U = 80^\circ \end{array}\]$

Take triangle ABC,

$\[\begin{array}{l}\angle A + \angle B + \angle C = 180^\circ \\ \Rightarrow 46^\circ + \angle B + 90^\circ = 180^\circ \\ \Rightarrow \angle B = 180^\circ - 136^\circ \\ \Rightarrow \angle B = 44^\circ \end{array}\]$

Take triangle PQR,

$\[\begin{array}{l}\angle P + \angle Q + \angle R = 180^\circ \\ \Rightarrow 51^\circ + \angle Q + 36^\circ = 180^\circ \\ \Rightarrow \angle Q = 180^\circ - 87^\circ \\ \Rightarrow \angle Q = 93^\circ \end{array}\]$

Hence the measure of $\[\angle U = 80^\circ ,\angle B = 44^\circ \]$ and $\[\angle Q = 93^\circ \]$,

Answer 2

Answer:

Measure of indicated angle in each triangle.

Step-by-step explanation:

To find: Measure of indicated angle.

Given: Other two angles in each triangle.

Solution:

We know , sum of three angles in a triangle is always 180°

So,

1st TRIANGLE

∠U+∠V+∠T =180°

∠U+63°+37° =180°

∠U= 180°-100°

∠U=80°

2ND TRIANGLE

∠A+∠B+∠C=180°

46°+90°+∠C =180°

∠C=44°

3rd TRIANGLE

∠R+∠P+∠Q= 180°

36°+51°+∠Q =180°

∠Q =93°

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