اختبار اختيار من متعدد تفاعلي: Angles of Triangles Quiz
This worksheet explores the fundamental properties of triangles, specifically focusing on the sum of interior angles and the exterior angle theorem. Students are required to apply geometric principles to solve for missing angle measures and determine the values of variables within triangular figures.
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اختبار شهادة تدريبي مؤقت للصف والمادة والفصل نفسه.
اختر إجابة واحدة لكل سؤال. عند الاختيار ستظهر النتيجة فورًا: الأخضر صحيح، والأحمر خطأ، وسيظهر تفسير الإجابة مباشرة إن كان متوفرًا. وبعد آخر سؤال ستظهر الدرجة النهائية تلقائيًا.
The sum of the measures of the interior angles of any triangle is always \(180^\circ\).
Question 2
Points: 1
Find the measure of the indicated angle.
Explanation
In the triangle shown, the sum of angles is \(180^\circ\). Thus, \(110^\circ + 25^\circ + x = 180^\circ\), which simplifies to \(135^\circ + x = 180^\circ\), so \(x = 45^\circ\).
Question 3
Points: 1
Find the measure of angle D.
Explanation
Using the triangle sum theorem, the missing angle D is calculated as \(180^\circ - (78^\circ + 62^\circ) = 180^\circ - 140^\circ = 40^\circ\).
Question 4
Points: 1
Find the missing angle.
Explanation
The figure is a \right triangle (indicated by the square symbol at U). Therefore, the missing angle is \(180^\circ - 90^\circ - 51^\circ = 39^\circ\).
Question 5
Points: 1
If two of the angles of a triangle are 30 and 70 degrees, the third angle measures...
Explanation
Subtract the sum of the given angles from \(180^\circ\): 180 - (30 + 70) = 180 - 100 = 80.
Question 6
Points: 1
Find the measure of the indicated angle.
Explanation
According to the exterior angle theorem, the exterior angle (BCD) is equal to the sum of the two remote interior angles: \(67^\circ + 35^\circ = 102^\circ\).
Question 7
Points: 1
Find the measure of the indicated angle.
Explanation
The exterior angle is \(150^\circ\). By the exterior angle theorem, \(61^\circ + \angle B = 150^\circ\). Therefore, \(\angle B = 150^\circ - 61^\circ = 89^\circ\).
Question 8
Points: 1
Solve for the missing angle with the question mark.
Explanation
The exterior angle is \(120^\circ\) and one remote interior angle is \(60^\circ\). The missing angle is \(120^\circ - 60^\circ = 60^\circ\).
Question 9
Points: 1
Which of the following angles can you add together to equal angle d?
Explanation
Based on the exterior angle theorem, the measure of an exterior angle (d) is equal to the sum of the measures of its two remote interior angles (a and b).
Question 10
Points: 1
Find the value of x.
Explanation
The exterior angle is \(105^\circ\). The remote interior angles are 12x and 9x. Thus, \(12x + 9x = 105 \implies 21x = 105 \implies x = 5\).
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